Can A True Believer Have An Evil Spirit?
Anyone who is not born again is in the dominion of Satan, and it is possible that an unregenerate person might have an evil spirit. I do not know how we would recognize that, but that is not the real problem.
The real problem is that anyone who is in an unregenerate state has been taken captive by satan to do his will (see 2 Timothy 2) and is in desperate need of spiritual rebirth.
Thus, the only solution to the problem is explained in the following verses of scripture:
2 Timothy 2:24
The servant of the Lord must not strive; but be gentle unto all [men], apt to teach, patient,
2 Timothy 2:25
In meekness instructing those that oppose themselves; if God peradventure will give them repentance to the acknowledging of the truth;
2 Timothy 2:26
And [that] they may recover themselves out of the snare of the devil, who are taken captive by him at his will.
At regeneration the elect sinner is taken out of the dominion and rule of Satan, and he is translated or moved into the kingdom of God. At regeneration, Satan has no power of any kind over us.
Thus to conclude it is impossible for a Christian to have an evil spirit.
Who hath delivered us from the power of darkness, and hath translated us into the kingdom of his dear Son.