Can Satan influence a Christian?

The answer is: Yes and No

No

When someone is "born again" they move from Satan's "dominion of darkness" into the "Kingdom of God's Son." Before they were converted they were under Satan's authority, since the "whole world is under the control of the evil one" but now they have been gloriously set free by Christ Jesus who defeated him on the cross. Praise God!

Yes

But can Satan influence a believer after he or she has come to Christ? The answer according to the New Testament is a resounding tragic yes. A believer cannot be possessed by the devil but they sure can be oppressed by the devil - and they can give Satan the "green light."

Here's a half dozen ways.....

(1) Sometimes God allows a Christian to be tested by the devil for a season
This happened to Job - a season of intense testing. The purpose is to glorify God and to refine the saint. The Lord Jesus himself was led into the wilderness to be tempted by the evil one, not to refine him for he was perfect but to gain the victory Adam lost.

(2) Sometime God allows a believer to experience a long-term thorn "messenger of Satan" to lead them to rest in God's power
The apostle Paul was given a "thorn in the flesh" (2 Cor 12) so that he would not become proud about the incredible insights he had been given but rather trust in God's almighty power. He called this thorn a "messenger of Satan" and as far as we can tell, it clung to him like a shadow.

(3) Anger gives Satan a green light
When a believer is angry, they give to Satan a foothold in their lives, according to Ephesians 4:26-27. We all know what this means: angry at one person can easily spill over to cross at everyone / unhappy with everything. 

(4) Disorder gives Satan a green light 
Satan hates the order God has wired into creation, and where ever there is disorder he finds a crack. If a man refuses to lead his wife, for example, or if a woman takes the lead in a marriage, Satan has found the perfect avenue of influence. Genesis 3 records the first of these opportunities. Eve took the lead, Adam backed out and Satan found his opportunity to pounce - and pounce he did. A disordered marriage is a green light for Satan.

(5) Opposition to church leaders makes a believer "captive to Satan's will"
A lesser-known way a believer can be influenced by Satan is if he or she opposes the leaders the Holy Spirit has appointed to lead the church. Paul says that all such must be gently instructed "in the hope that they will come to their senses and escape the trap of the devil who has taken them captive to do his will." (2 Tim 2:25-26). That is pretty serious! A Christian can become not a captive to Satan, but a captive to his will.

(6) When we rebel against God's will - especially God's will for suffering
Good disciple Peter told Jesus that he would not suffer the agonies of the cross. Jesus replied to him, "Get behind me Satan." At that moment, when Peter resisted God's will for Jesus' life - and especially his will for suffering  - he became a spokesperson for Satan.

In our western evangelicalism whose rationalism can easily filter out all talk of the supernatural, whether of God or Satan, we can easily disregard the influence of Satan upon us. But these six avenues of influence reveal how pernicious the evil one is and remind us of our need every day to pray "Deliver us from the Evil one."