According to baptists can a Christian be demon possessed?

Baptists are trinitarian and believe that God the Holy Spirit enters into and permanently lives within every individual who repents of their sin and believes that Jesus is the Son of God. Both the individual body of the believer and the corporate "body" of all believers become the temple of the Holy Spirit upon receiving salvation in the name of Christ.

Baptists believe in the existence of Satan and demons and in the reality of spiritual warfare. They believe that persons can be literally possessed by demons and that it is the power of the gospel that can expel this and every other affliction that the unredeemed suffer.

Baptists do not hold that a true believer can be possessed by a demonic entity for the simple reason that the demon would first have to overcome the Spirit of Almighty God who lives within that person:

And the scribes who came down from Jerusalem were saying, “He is possessed by Beelzebul,” and “by the prince of demons he casts out the demons.” And he called them to him and said to them in parables, “How can Satan cast out Satan? If a kingdom is divided against itself, that kingdom cannot stand. And if a house is divided against itself, that house will not be able to stand. And if Satan has risen up against himself and is divided, he cannot stand, but is coming to an end. But no one can enter a strong man's house and plunder his goods, unless he first binds the strong man. Then indeed he may plunder his house. - Mark 3:22-27

While this parable is spoken against those who accused Jesus of casting out demons (which they could not deny) by demonic rather than divine power the thrust holds true for the believer as well. The believer is "in" Christ, is seated with Christ in heavenly places, and Christ (arguably the strongest man) is within the believer.

Believers can be beleaguered, badgered, afflicted, and harassed by demonic entities. Through disobedience, poor teaching, unhealthy fellowship, etc. believers can open themselves up to increased demonic harassment and can allow footholds and strongholds for the enemy within their thoughts and behavior. Conversely a life of faith and obedience can also invite demonic oppression as the evil ones hate the life of Christ being manifested.

Satan is the God of this world and is blinding the minds of unbelievers:

Therefore, having this ministry by the mercy of God, we do not lose heart. But we have renounced disgraceful, underhanded ways. We refuse to practice cunning or to tamper with God's word, but by the open statement of the truth we would commend ourselves to everyone's conscience in the sight of God. And even if our gospel is veiled, it is veiled to those who are perishing. In their case the god of this world has blinded the minds of the unbelievers, to keep them from seeing the light of the gospel of the glory of Christ, who is the image of God. - 2 Corinthians 4:1-4

Satan is the prince of the power of the air and holds sway over the thoughts and activities of those outside of Christ:

And you were dead in the trespasses and sins in which you once walked, following the course of this world, following the prince of the power of the air, the spirit that is now at work in the sons of disobedience— among whom we all once lived in the passions of our flesh, carrying out the desires of the body and the mind, and were by nature children of wrath, like the rest of mankind. - Ephesians 2:1-3

Satan (like a lion) hunts for those believers he may devour (that is, swallow up the testimony of) through affliction and suffering:

Humble yourselves, therefore, under the mighty hand of God so that at the proper time he may exalt you, casting all your anxieties on him, because he cares for you. Be sober-minded; be watchful. Your adversary the devil prowls around like a roaring lion, seeking someone to devour. Resist him, firm in your faith, knowing that the same kinds of suffering are being experienced by your brotherhood throughout the world. - 1 Peter 5:6-9

But Satan cannot possess a believer because he cannot bind or cast out Christ within the believer:

Beloved, do not believe every spirit, but test the spirits to see whether they are from God, for many false prophets have gone out into the world. By this you know the Spirit of God: every spirit that confesses that Jesus Christ has come in the flesh is from God, and every spirit that does not confess Jesus is not from God. This is the spirit of the antichrist, which you heard was coming and now is in the world already.  Little children, you are from God and have overcome them, for he who is in you is greater than he who is in the world. - 1 John 4:1-4

My sheep hear my voice, and I know them, and they follow me. I give them eternal life, and they will never perish, and no one will snatch them out of my hand. My Father, who has given them to me, is greater than all, and no one is able to snatch them out of the Father's hand. I and the Father are one.” - John 10:27-30

According to Baptist teaching, believers are secure both within and without because, in God's economy, they have already been raised with Christ:

If then you have been raised with Christ, seek the things that are above, where Christ is, seated at the right hand of God. Set your minds on things that are above, not on things that are on earth. For you have died, and your life is hidden with Christ in God. - Colossians 3:1-3

Not according to this source.

Can a Christian be demon possessed? No,” Southern Baptist Theological Seminary theology professor Stephen Wellum said in a video posted on the seminary’s website Feb. 28. “To be demon possessed would mean one is outside of Christ, one is dead in their sins, one is under the power of the evil one.

Further in that article we find

Following a 2010 meeting on exorcism organized by Catholic bishops in Baltimore, Southern Seminary President R. Albert Mohler Jr. explained why evangelicals “do not have a rite of exorcism, like those prescribed by the Catholic Church, in which clergy members recite prescribed words to supposedly drive away a demon. “To adopt such an invention would be to surrender the high ground of the Gospel,” Mohler wrote in a commentary. “We are engaged in spiritual warfare every minute of every day, whether we recognize it or not.” Proclamation of the Gospel, Mohler said, is the church’s greatest weapon against demon possession. “There is nothing the demons fear or hate more than evangelism and missions, where the Gospel pushes back with supernatural power against their possessions, rendering them impotent and powerless,” Mohler wrote. “Every time a believer shares the Gospel and declares the name of Jesus, the demons and the Devil lose their power.”