Here are two Bible verses on the subject. One suggests that perhaps Jesus did perform baptism:
After this, Jesus and his disciples went out into the Judean countryside, where he spent some time with them, and baptised (Matthew 3:22).
However, the following Bible verse says it was Jesus’ disciples who did the baptising:
The Pharisees heard that Jesus was gaining and baptising more disciples than John, although in fact it was not Jesus who baptised, but his disciples (Matthew 4:1).
The Bible does not tell us if Jesus baptised anyone, or why he would not baptise anyone. Perhaps it was to avoid a situation where a person baptised by Jesus would think they were superior to other believers based who had been baptised by a disciple.
An example of this is recorded in 1 Corinthians 1:12-15 where the apostle Paul had cause to rebuke believers who made a big thing out of who had baptised them. Some were quarrelling over who had baptised them, saying they followed Apollos, or Cephas, or Christ.
Is Christ divided? Was Paul crucified for you? Were you baptised into the name of Paul?
The important point is not who does the baptising, but being baptised into the name of Christ. Also, John the Baptist predicted that the Messiah would baptise with Holy Spirit and fire, not water:
I baptise you with water for repentance, but he who is coming after me is mightier than I, whose sandals I am not worthy to carry. He will baptise you with the Holy Spirit and fire. (Matthew 3:11)
Neither Matthew 3:11 nor Matthew 3:14 say if Jesus himself baptised anyone, only that a time would come (after Jesus’ death and resurrection) when he would send the Comforter, the Holy Spirit, to empower his followers to spread the gospel message throughout the world. First Corinthians 12:13 says:
We were all baptised by one Spirit so as to form one body—whether Jews or Gentiles, slave or free—and we were all given the one Spirit to drink.”
