Saint Polycarp of Antioch is not a patron saint. Polycarp of Smyrna is the patron saint against dysentery and against earache.
There are at least two saints named Polycarp and both died as martyrs which made them saints in the eyes of the early Christian community.
Polycarp of Smyrna was stabbed to death c.155 at Smyrna and his body burned.
Saint Polycarp of Antioch was martyred at Antioch - date unknown.
Peter and Paul were saints only in the New Testament meaning of the word. Canonization by the church does not make anyone a saint except in the eyes of man. In the New Testament the Greek word hagios...