There are only a handful of passages in which Paul mentions Satan.Here he is an evil spirit whose raison d’etre is to frustrate the spread of Paul’s gospel. In 1 Cor 5, the apostle instructs the Corinthians to hand over to Satan the man who was caught in fornication. Here Satan’s domain is that of unbelief and the failure of the Gospel.
I can find no suggestion in the “authentic” epistles that Satan is a cosmic power, ruler, authority, “prince of the power of the air,” or what have you. It is only non-Pauline texts that make the identification of Satan as the evil ruler of this world.
Paul’s References to Satan/Belial
It should be noted that no reference is found in Galatians.
In Romans 16:20 we read
But in context, this belongs to an exhortation against schism and heresy.The God of peace will shortly crush Satan under your feet. (Rom 16:20)
Other references to Satan/Belial—
1 Cor 7:5
Stop depriving one another, except by agreement for a time so that you may devote yourselves to prayer, and come together again so that Satan will not tempt you because of your lack of self-control.
2 Cor 2:10-11
But one whom you forgive anything, I also forgive; for indeed what I have forgiven, if I have forgiven anything, I did so for your sakes in the presence of Christ, so that no advantage would be taken of us by Satan, for we are not ignorant of his schemes.
2 Cor 6:14-16
Do not be mismatched with unbelievers; for what do righteousness and lawlessness share together, or what does light have in common with darkness? Or what harmony does Christ have with Belial, or what does a believer share with an unbeliever? Or what agreement does the temple of God have with idols?
2 Cor 11:14
For such men are false apostles, deceitful workers, disguising themselves as apostles of Christ. No wonder, for even Satan disguises himself as an angel of light. Therefore it is not surprising if his servants also disguise themselves as servants of righteousness, whose end will be according to their deeds.
2 Cor 12:7
Because of the extraordinary greatness of the revelations, for this reason, to keep me from exalting myself, there was given to me a thorn in the flesh, a messenger of Satan to torment me—to keep me from exalting myself!
That’s all there is (did I miss anything?). The reference is always practical. Paul’s adversary never rises in power or greatness or authority above the apostle himself.1 Thss 2:18
For we wanted to come to you—I, Paul, more than once—and Satan hindered us.
We are accustomed to magnify the power of Satan simply because every other major part of the NT, including those Pauline epistles that are now deemed inauthentic or forged, seeks to identify him that way. In Neil Forsythe’s magisterial history The Old Enemy: Satan & the Combat Myth, Paul is considered “circumspect” in his references to the evil one. I think that’s a misleading way to say that the classic Christian myth of Satan is essentially a post-Pauline production.
If we consider the four groupings of the NT material in the tradition
1. Gospels
2. Pauline corpus
3. Acts & General Epistles
4. Revelation
it is evident that Satan looms large, indeed he is the ruling prince of darkness and evil, in groups 1, 3, and 4. We see him doing battle with Jesus directly in the Gospels. In Luke and John, he enters into Judas and brings about Jesus' death. In Acts, at Paul's trial before Festus, we see him attributing to the risen Jesus the statement that Paul is being sent to the gentiles in order to "open their eyes so that they may turn from darkness to light and from the power of Satan to God..." (Acts 26:18). For the writer of 1 John, "the whole world lies under the power of the evil one" (5:19). Finally, in Revelation, Satan attains full cosmic power. In 2 Thessalonians, Ephesians, and the Pastorals, we also find a powerful fire-breathing Devil. But this figure is absent from those epistles that are deemed earliest in the tradition.