I do not see anything in the word of God that teaches or shows a Born- again Christian Spirit-filled can be demon-possessed.
There are no examples of one after the resurrected Lord and His ascension. Nor were chritians saved until HIS resurrection.
Ananias having the influence of Satan in his heart did not mean he was possessed by the devil. Peter was told by Jesus that flesh and blood did not reveal to him who Jesus is when asked by the Lord.
Not too many verses in that same chapter, Jesus tells Satan to get behind me as he spoke to Peter. That rebuke was not a possession of the devil in Peter but of one of the flesh from Peter if satan had possessed Peter would not have Jesus said Come out of HIM as HE DID IN EVER situation where a person was demon-possessed?
Satan certainly put the idea into Peter's head. But no, he was not possessed. There are different degrees of bondage to demons. Very few people are possessed in the sense of having no control at all. Those people usually seek to be possessed in order to receive more of Satan's power.
There is a reason why we are commanded to resist the devil. If we do not, we will become more and more controlled by his agents, which are demons and evil spirits. We do not wrestle with flesh and blood. The battle is primarily in the mind. Demons have access to the mind of man. They will float thoughts into the mind of a Christian, hoping to get his agreement .Those thoughts will match the personality of a person. The more self confident will be tempted with thoughts of grandiose schemes of leading revival, TV ministry or great success in ministry. The more introverted and self focused will be put down, reminded of failure and told how hopeless they are.
Evil spirits and demons occupy the soul, with the intent of controlling the will. In some cases, the demon can be driven out and the victory won. In others, it is necessary to push back against the evil spirits until they relinquish their hold.
Maybe an example will help. I, like most men, was bound by a lust demon. I became more and more oppressed until I had imaginations like porno movies running through my mind continually. I met a Pastor who had a number of the gifts of the Spirit, including discernment of spirits. He told me my problem even though I'd said nothing - I was too ashamed. I agreed and he cast the demon out of me. The "movies" stopped immediately.
From then on, I had to resist the imaginations that came from time to time. It was nothing like before, but I did not want to be captured again.
I had another problem that had to be dealt with differently. It was passivity, a polite word for laziness. It translates as "can't be bothered" in practice. It was a gradual descent, like a creeping paralysis. I'd have things to do but I kept putting them off. I spoke to the pastor about it. He'd suffered from the same problem. He was a most active man usually, but passivity had grabbed hold of him at one time.
In this case, the answer was to get active again. I started doing things for the sake of it. I had to force myself to say that "later" was too late. Proverbs has good things to say about this. It took a while to become passive and it was a long road back to normal.
Satan and God are both after the same thing. That is the cooperation of man's will. Satan will do anything, lie, deceive, threaten, promise, he has no scruples. God does everything according to His holy character and righteous nature. God never violates our will. Satan tries to coerce us all the time.
Our enemy is ignorance. The war is won already. But we must enforce the victory for ourselves, and sometimes for the brethren. Ignorance is not bliss, it is dangerous. God's people are still being destroyed because of their lack of knowledge.