Excerpt from
www.bible-history.com:
This magnificent synagogue was made of white limestone and wonderfully ornamented. Archeologists have determined that the 2-story synagogue was built around the beginning of the third century A.D., because of its architectural style, decorations, and inscriptions. Therefore it was not the synagogue in which Jesus taught, although it was most likely built upon the same site as the first century synagogue.
The gospel of John reveals that it was here in which Jesus taught that he was the true bread of life coming down out of heaven, after feeding the 5000 (John 6:59). Shortly after he was rejected in Capernaum because he had healed on the Sabbath day, which the Jewish authorities considered blasphemy. He often taught on their hillsides and near the sea of Galilee. But it was at Capernaum where Jesus and his disciples loved to come. It was probably here at Capernaum were Jesus raised Jairus's daughter from the dead (Mark 5:21-43), and it was also here that Jesus taught his disciples about being childlike and he brought a child into the midst of them (Mark 9: 33-37). Also at Capernaum Jesus spoke with Peter about paying the Temple tax sending him to catch a fish to pay for it (Matthew 17:24-27).