Did the apostle Paul meet Jesus?

No, Paul and Jesus never met while Jesus was still alive. It was after Jesus rose from the dead that Jesus appeared to Paul (See 1 Corinthians 15:8).

While some people interpret Paul as having a vision on the road to Damascus (Acts 9 1-6), Paul himself insisted that Jesus appeared to him in his resurrected person in his written Word (See 1 Corinthians 15:8).