You are either misunderstanding or misinterpreting this Scripture, so let's take a close look ant what was actually written by Paul:
In meekness instructing those that oppose themselves; if God peradventure will give them repentance to the acknowledging of the truth; And that they may recover themselves out of the snare of the devil, who are taken captive by him at his will.
1. We are told that there were some Christians who were opposing the truth and they were to be instructed in meekness.
2. It was Paul's hope that God would bring them to repentance so that they would acknowledge the truth and abandon the lies.
3. The lies were created by Satan and had become the snare (or trap) of the Devil to entrap the minds of these Christians in lies opposed to God's truth.
4. Because these Christians had been ensnared or entrapped in lies, they had become captives of Satan at his will. In other words, Satan had desired to trap some Christians in lies which opposed God' truth, and because they preferred the lies to the truth, they were trapped. Therefore it was Paul's desire to see them freed from this snare by having Timothy instruct them in the truth, so that they would repent -- turn away form the lies -- and acknowledge the truth without any reservation.
There is no way that this can be interpreted as the Christians being demon-possessed. We currently have a thread about "Some misconceptions about God" where some Christians have been snared by the lies of the Devil spoken through false teachers. There is no way that one can this demon-possession. They are simply deceived, and if they will not repent then they will continue to be deceived by Satan.