I know that there are those who would say “yes.” They have their first-hand stories claiming demon possession of a Christian. The first thing I think about, though, is 1 john 4: 4. “Greater is He who is in you than he who is in the world.”
Then I couple that with Matthew 12: 29. “How can anyone enter the strong man’s house and carry off his property, unless he first binds the strong man? And then he will plunder his house.”
I add to that Jesus’ response to some antagonistic Jews in John 8: 48, 49. They had accused Him of being demon possessed. Jesus answered, “I do not have a demon; but I honor My Father, and you dishonor Me.”
Looking at these three scriptural passages, here’s the picture that emerges to me.
To begin with, a true Christian desires and endeavors to honor God by surrendering and allowing God’s indwelling work to be carried out according to His will for His pleasure. Under such circumstances, a demon could not possibly enter the body, overcome and stop such works. God is more powerful than any and even all demons combined.
As such, and furthering that thought, I flip Matthew 12: 29. It references a demon as the strong man within a possessed unbeliever. But in the case of a believer, the indwelling Spirit is God. God is the strong man. He can’t be bound. Therefore a demon can’t enter His domain to plunder what is of God.
Finally, for what it’s worth, I can’t find a single biblical instance of a believer being possessed. The demon-possessed characters that are mentioned were not of Christ at the time.