Paul Was the Apostle to the Gentiles
The apostle Paul was sent to the Gentiles while Peter and the others went to the Jews.
On the contrary, they saw that I had been entrusted with the task of preaching the gospel to the Gentiles, just as Peter had been to the Jews. For God, who was at work in the ministry of Peter as an apostle to the Jews, was also at work in my ministry as an apostle to the Gentiles. James, Peter and John, those reputed to be pillars, gave me and Barnabas the right hand of fellowship when they recognized the grace given to me. They agreed that we should go to the Gentiles, and they to the Jews. (Galatians 2:7-9)
Baptism Was Not Part of the Gospel for the Gentiles
However, Paul's message, which was for the Gentiles, did not include baptism. The Jews who had been practicing the law with its ceremonial washings for hundreds of years (with the purpose of pointing them to the coming Messiah) needed one last washing for closure. But the Gentiles didn't. They needed a relationship with God without all the religious trappings.
I am thankful that I did not baptize any of you except Crispus and Gaius, so no one can say that you were baptized into my name. (Yes, I also baptized the household of Stephanas; beyond that, I don't remember if I baptized anyone else.)
For Christ did not send me to baptize, but to preach the gospel-- not with words of human wisdom, lest the cross of Christ be emptied of its power. (1 Corinthians 1:12-17)
But Paul did baptize Gentiles in Corinth didn't he?
Not necessarily. The account of his being in Corinth is found in Acts 18. It starts out stating that Paul went there to visit some Jewish friends that had escaped from Rome.
After this, Paul left Athens and went to Corinth. There he met a Jew named Aquila, a native of Pontus, who had recently come from Italy with his wife Priscilla, because Claudius had ordered all the Jews to leave Rome. Paul went to see them, and because he was a tentmaker as they were, he stayed and worked with them.(Acts 18:1-3)
One of the names of the people that Paul baptized was Crispus who must have been a Jew since he was the synagogue ruler!
Crispus, the synagogue ruler, and his entire household believed in the Lord; and many of the Corinthians who heard him believed and were baptized. (Acts 18:8)
The account in Acts refers only to Jews. Does that mean that he didn't baptize any Gentiles? We don't know for certain --he did baptize these Jewish friends-- but it's doubtful since he said that his gospel was for the Gentiles and it did not include baptism.
