Jesus is God

Since, also, there is but one unbegotten Being, God, even the Father; and one only-begotten Son, God, the Word and man; and one Comforter, the Spirit of truth; and also one preaching, and one faith, and one baptism;
The Epistle of Ignatius to the Philadelphians Chapter IV​

But the Holy Spirit does not speak His own things, but those of Christ, and that not from himself, but from the Lord; even as the Lord also announced to us the things that He received from the Father. For, says He, “the word which ye hear is not Mine, but the Father’s, who sent Me.” And says He of the Holy Spirit, “He shall not speak of Himself, but whatsoever things He shall hear from Me.” And He says of Himself to the Father, “I have,” says He, “glorified Thee upon the earth; I have finished the work which, Thou gavest Me; I have manifested Thy name to men.” And of the Holy Ghost, “He shall glorify Me, for He receives of Mine.”
The Epistle of Ignatius to the Ephesians Chapter IX​

For if there is one God of the universe, the Father of Christ, “of whom are all things;” and one Lord Jesus Christ, our [Lord], “by whom are all things;” and also one Holy Spirit, who wrought in Moses, and in the prophets and apostles;
The Epistle of Ignatius to the Philippians Chapter I​

For, in the name of God, the Father and Lord of the universe, and of our Saviour Jesus Christ, and of the Holy Spirit, they then receive the washing with water.
The First Apology Chapter LXI​

The Church, though dispersed through our the whole world, even to the ends of the earth, has received from the apostles and their disciples this faith: [She believes] in one God, the Father Almighty, Maker of heaven, and earth, and the sea, and all things that are in them; and in one Christ Jesus, the Son of God, who became incarnate for our salvation; and in the Holy Spirit, who proclaimed through the prophets the dispensations of God, and the advents, and the birth from a virgin, and the passion, and the resurrection from the dead, and the ascension into heaven in the flesh of the beloved Christ Jesus, our Lord, and His [future] manifestation from heaven in the glory of the Father “to gather all things in one,” . . .
Against Heresies Book I Chapter X​

The rule of truth which we hold, is, that there is one God Almighty, who made all things by His Word, and fashioned and formed, out of that which had no existence, all things which exist. Thus saith the Scripture, to that effect “By the Word of the Lord were the heavens established, and all the might of them, by the spirit of His mouth.” And again, “All things were made by Him, and without Him was nothing made.” There is no exception or deduction stated; but the Father made all things by Him, whether visible or invisible, objects of sense or of intelligence, temporal, on account of a certain character given them, or eternal; and these eternal things He did not make by angels, or by any powers separated from His Ennœa.
For God needs none of all these things, but is He who, by His Word and Spirit, makes, and disposes, and governs all things, and commands all things into existence,—He who formed the world (for the world is of all),—He who fashioned man,—He [who] is the God of Abraham, and the God of Isaac, and the God of Jacob, above whom there is no other God, nor initial principle, nor power, nor pleroma,—He is the Father of our Lord Jesus Christ, as we shall prove.
Book I Chapter XXII​

Therefore neither would the Lord, nor the Holy Spirit, nor the apostles, have ever named as God, definitely and absolutely, him who was not God, unless he were truly God; nor would they have named any one in his own person Lord, except God the Father ruling over all, and His Son who has received dominion from His Father over all creation, as this passage has it: “The Lord said unto my Lord, Sit Thou at my right hand, until I make Thine enemies Thy footstool.” Here the [Scripture] represents to us the Father addressing the Son; He who gave Him the inheritance of the heathen, and subjected to Him all His enemies. Since, therefore, the Father is truly Lord, and the Son truly Lord, the Holy Spirit has fitly designated them by the title of Lord.
Against Heresies Book III Chapter VI​

For with Him were always present the Word and Wisdom, the Son and the Spirit, by whom and in whom, freely and spontaneously, He made all things, to whom also He speaks, saying, “Let Us make man after Our image and likeness;” He taking from Himself the substance of the creatures [formed], and the pattern of things made, and the type of all the adornments in the world.
Against Heresies Book IV Chapter XX​

O mystic marvel! The universal Father is one, and one the universal Word; and the Holy Spirit is one and the same everywhere, . . .
The Instructor. Book I Chapter VI​

In the course of time, then, the Father forsooth was born, and the Father suffered, God Himself, the Lord Almighty, whom in their preaching they declare to be Jesus Christ. We, however, as we indeed always have done (and more especially since we have been better instructed by the Paraclete, who leads men indeed into all truth), believe that there is one only God, but under the following dispensation, or οἰκονομία , as it is called, that this one only God has also a Son, His Word, who proceeded from Himself, by whom all things were made, and without whom nothing was made. Him we believe to have been sent by the Father into the Virgin, and to have been born of her—being both Man and God, the Son of Man and the Son of God, and to have been called by the name of Jesus Christ; we believe Him to have suffered, died, and been buried, according to the Scriptures, and, after He had been raised again by the Father and taken back to heaven, to be sitting at the right hand of the Father, and that He will come to judge the quick and the dead; who sent also from heaven from the Father, according to His own promise, the Holy Ghost, the Paraclete, the sanctifier of the faith of those who believe in the Father, and in the Son, and in the Holy Ghost.
But keeping this prescriptive rule inviolate, still some opportunity must be given for reviewing (the statements of heretics), with a view to the instruction and protection of divers persons; were it only that it may not seem that each perversion of the truth is condemned without examination, and simply prejudged; especially in the case of this heresy, which supposes itself to possess the pure truth, in thinking that one cannot believe in One Only God in any other way than by saying that the Father, the Son, and the Holy Ghost are the very selfsame Person. As if in this way also one were not All, in that All are of One, by unity (that is) of substance; while the mystery of the dispensation is still guarded, which distributes the Unity into a Trinity, placing in their order the three Persons—the Father, the Son, and the Holy Ghost: three, however, not in condition, but in degree; not in substance, but in form; not in power, but in aspect; yet of one substance, and of one condition, and of one power, inasmuch as He is one God, from whom these degrees and forms and aspects are reckoned, under the name of the Father, and of the Son, and of the Holy Ghost. How they are susceptible of number without division, will be shown as our treatise proceeds.
Against Praxeas Chapter II​

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The simple, indeed, (I will not call them unwise and unlearned,) who always constitute the majority of believers, are startled at the dispensation (of the Three in One), on the ground that their very rule of faith withdraws them from the world’s plurality of gods to the one only true God; not understanding that, although He is the one only God, He must yet be believed in with His own οἰκονομία . The numerical order and distribution of the Trinity they assume to be a division of the Unity; whereas the Unity which derives the Trinity out of its own self is so far from being destroyed, that it is actually supported by it. They are constantly throwing out against us that we are preachers of two gods and three gods, while they take to themselves pre-eminently the credit of being worshippers of the One God; just as if the Unity itself with irrational deductions did not produce heresy, and the Trinity rationally considered constitute the truth.
Against Praxeas Chapter III​

But as for me, who derive the Son from no other source but from the substance of the Father, and (represent Him) as doing nothing without the Father’s will, and as having received all power from the Father, how can I be possibly destroying the Monarchy from the faith, when I preserve it in the Son just as it was committed to Him by the Father? The same remark (I wish also to be formally) made by me with respect to the third degree in the Godhead, because I believe the Spirit to proceed from no other source than from the Father through the Son.
Against Praxeas Chapter IV​

Bear always in mind that this is the rule of faith which I profess; by it I testify that the Father, and the Son, and the Spirit are inseparable from each other, and so will you know in what sense this is said. Now, observe, my assertion is that the Father is one, and the Son one, and the Spirit one, and that They are distinct from Each Other. This statement is taken in a wrong sense by every uneducated as well as every perversely disposed person, as if it predicated a diversity, in such a sense as to imply a separation among the Father, and the Son, and the Spirit.
I am, moreover, obliged to say this, when (extolling the Monarchy at the expense of the Economy) they contend for the identity of the Father and Son and Spirit, that it is not by way of diversity that the Son differs from the Father, but by distribution: it is not by division that He is different, but by distinction; because the Father is not the same as the Son, since they differ one from the other in the mode of their being. For the Father is the entire substance, but the Son is a derivation and portion of the whole, as He Himself acknowledges: “My Father is greater than I.” In the Psalm His inferiority is described as being “a little lower than the angels.” Thus the Father is distinct from the Son, being greater than the Son, inasmuch as He who begets is one, and He who is begotten is another; He, too, who sends is one, and He who is sent is another; and He, again, who makes is one, and He through whom the thing is made is another.
Happily the Lord Himself employs this expression of the person of the Paraclete (Holy Spirit), so as to signify not a division or severance, but a disposition (of mutual relations in the Godhead); for He says, “I will pray the Father, and He shall send you another Comforter…even the Spirit of truth,” thus making the Paraclete distinct from Himself, even as we say that the Son is also distinct from the Father; so that He showed a third degree in the Paraclete, as we believe the second degree is in the Son, by reason of the order observed in the Economy. Besides, does not the very fact that they have the distinct names of Father and Son amount to a declaration that they are distinct in personality? For, of course, all things will be what their names represent them to be; and what they are and ever will be, that will they be called; and the distinction indicated by the names does not at all admit of any confusion, because there is none in the things which they designate. “Yes is yes, and no is no; for what is more than these, cometh of evil.”
Against Praxeas Chapter IX​

From all which we learn that the person of the Holy Spirit was of such authority and dignity, that saving baptism was not complete except by the authority of the most excellent Trinity of them all, i.e., by the naming of Father, Son, and Holy Spirit, and by joining to the unbegotten God the Father, and to His only-begotten Son, the name also of the Holy Spirit.
. . .
Nevertheless it seems proper to inquire what is the reason why he who is regenerated by God unto salvation has to do both with Father and Son and Holy Spirit, and does not obtain salvation unless with the co-operation of the entire Trinity; and why it is impossible to become partaker of the Father or the Son without the Holy Spirit.
Origen De Principiis. Book I Chapter III​

But in our desire to show the divine benefits bestowed upon us by Father, Son, and Holy Spirit, which Trinity is the fountain of all holiness, we have fallen, in what we have said, into a digression, having considered that the subject of the soul, which accidentally came before us, should be touched on, although cursorily, seeing we were discussing a cognate topic relating to our rational nature. We shall, however, with the permission of God through Jesus Christ and the Holy Spirit, more conveniently consider in the proper place the subject of all rational beings, which are distinguished into three genera and species.
Origen De Principiis. Book I Chapter IV​

For the end is always like the beginning: and, therefore, as there is one end to all things, so ought we to understand that there was one beginning; and as there is one end to many things, so there spring from one beginning many differences and varieties, which again, through the goodness of God, and by subjection to Christ, and through the unity of the Holy Spirit, are recalled to one end, which is like unto the beginning: all those, viz., who, bending the knee at the name of Jesus, make known by so doing their subjection to Him: and these are they who are in heaven, on earth, and under the earth: by which three classes the whole universe of things is pointed out, those, viz., who from that one beginning were arranged, each according to the diversity of his conduct, among the different orders, in accordance with their desert; for there was no goodness in them by essential being, as in God and His Christ, and in the Holy Spirit. For in the Trinity alone, which is the author of all things, does goodness exist in virtue of essential being; while others possess it as an accidental and perishable quality, and only then enjoy blessedness, when they participate in holiness and wisdom, and in divinity itself.
Origen De Principiis. Book I Chapter VI​

After these points, now, we proved to the best of our power in the preceding pages that all things which exist were made by God, and that there was nothing which was not made, save the nature of the Father, and the Son, and the Holy Spirit; and that God, who is by nature good, desiring to have those upon whom He might confer benefits, and who might rejoice in receiving His benefits, created creatures worthy (of this), i.e., who were capable of receiving Him in a worthy manner, who, He says, are also begotten by Him as his sons. He made all things, moreover, by number and measure. For there is nothing before God without either limit or measure. For by His power He comprehends all things, and He Himself is comprehended by the strength of no created thing, because that nature is known to itself alone. For the Father alone knoweth the Son, and the Son alone knoweth the Father, and the Holy Spirit alone searcheth even the deep things of God.
Origen De Principiis. Book IV Chapter I.35​

If the heavenly virtues, then, partake of intellectual light, i.e., of divine nature, because they participate in wisdom and holiness, and if human souls, have partaken of the same light and wisdom, and thus are mutually of one nature and of one essence,—then, since the heavenly virtues are incorruptible and immortal, the essence of the human soul will also be immortal and incorruptible. And not only so, but because the nature of Father, and Son, and Holy Spirit, whose intellectual light alone all created things have a share, is incorruptible and eternal, it is altogether consistent and necessary that every substance which partakes of that eternal nature should last for ever, and be incorruptible and eternal, so that the eternity of divine goodness may be understood also in this respect, that they who obtain its benefits are also eternal. But as, in the instances referred to, a diversity in the participation of the light was observed, when the glance of the beholder was described as being duller or more acute, so also a diversity is to be noted in the participation of Father, Son, and Holy Spirit, varying with the degree of zeal or capacity of mind.
Origen De Principiis. Book IV Chapter I.36​

The individual names uttered by me can neither be separated from one another, nor parted. I spoke of the Father, and before I made mention of the Son I already signified Him in the Father. I added the Son; and the Father, even although I had not previously named Him, had already been absolutely comprehended in the Son. I added the Holy Spirit; but, at the same time, I conveyed under the name whence and by whom He proceeded. But they are ignorant that neither the Father, in that He is Father, can be separated from the Son, for that name is the evident ground of coherence and conjunction; nor can the Son be separated from the Father, for this word Father indicates association between them. And there is, moreover, evident a Spirit who can neither be disjoined from Him who sends, nor from Him who brings Him. How, then, should I who use such names think that these are absolutely divided and separated the one from the other?
(After a few words he adds:—)
Thus, indeed, we expand the indivisible Unity into a Trinity; and again we contract the Trinity, which cannot be diminished, into a Unity.
(From the Same Second Book.)
In the beginning was the Word. But that was not the Word which produced the Word. For “the Word was with God.” The Lord is Wisdom; it was not therefore Wisdom that produced Wisdom; for “I was that” says He, “wherein He delighted.” Christ is truth; but “blessed,” says He, “is the God of truth.”
(The Conclusion of the Entire Treatise.)
In accordance with all these things, the form, moreover, and rule being received from the elders who have lived before us, we also, with a voice in accordance with them, will both acquit ourselves of thanks to you, and of the letter which we are now writing. And to God the Father, and His Son our Lord Jesus Christ, with the Holy Spirit, be glory and dominion for ever and ever. Amen.
The Works of Dionysius. Extant Fragments. Part I Chapter IV​

Finally, when, after the resurrection, the apostles are sent by the Lord to the heathens, they are bidden to baptize the Gentiles “in the name of the Father, and of the Son, and of the Holy Ghost.” How, then, do some say, that a Gentile baptized without, outside the Church, yea, and in opposition to the Church, so that it be only in the name of Jesus Christ, everywhere, and in whatever manner, can obtain remission of sin, when Christ Himself commands the heathen to be baptized in the full and united Trinity?
Epistle LXXII.5.18​

And now, indeed, concerning the Father, and the Son, and the Holy Spirit, let it be sufficient to have briefly said thus much, and to have laid down these points concisely, without carrying them out in a lengthened argument. For they could be presented more diffusely and continued in a more expanded disputation, since the whole of the Old and New Testaments might be adduced in testimony that thus the true faith stands. But because heretics, ever struggling against the truth, are accustomed to prolong the controversy of pure tradition and Catholic faith, being offended against Christ; because He is, moreover, asserted to be God by the Scriptures also, and this is believed to be so by us; we must rightly—that every heretical calumny may be removed from our faith—contend, concerning the fact that Christ is God also, in such a way as that it may not militate against the truth of Scripture; nor yet against our faith, how there is declared to be one God by the Scriptures, and how it is held and believed by us.
A Treatise of Novatian Concerning the Trinity. Chapter XXX.​

Therefore, when the holy prophets, and all, as I have said, who righteously and justly walked in the law of the Lord, together with the entire people, celebrated a typical and shadowy Passover, the Creator and Lord of every visible and invisible creature, the only-begotten Son, and the Word co-eternal with the Father and the Holy Spirit, and of the same substance with them, according to His divine nature, our Lord and God, Jesus Christ, . .
Epistles on the Arian Heresy And the Deposition of Arius. Chapter I.7​

Therefore to the unbegotten Father, indeed, we ought to preserve His proper dignity, in confessing that no one is the cause of His being; but to the Son must be allotted His fitting honour, in assigning to Him, as we have said, a generation from the Father without beginning, and allotting adoration to Him, so as only piously and properly to use the words, “He was,” and “always,” and “before all worlds,” with respect to Him; by no means rejecting His Godhead, but ascribing to Him a similitude which exactly answers in every respect to the Image and Exemplar of the Father. But we must say that to the Father alone belongs the property of being unbegotten, for the Saviour Himself said, “My Father is greater than I.” And besides the pious opinion concerning the Father and the Son, we confess to one Holy Spirit, as the divine Scriptures teach us; who hath inaugurated both the holy men of the Old Testament, and the divine teachers of that which is called the New.
Epistles on the Arian Heresy And the Deposition of Arius. Chapter I.12​