Matthew calls Capernaum Jesus’ own city,
where he lived (Matthew 4:13), probably in Peter’s house (see Mark 2:1). Having lived there for twelve months, he had become a citizen of the city, so indeed it was his
(idian) city, to which he returned from his visit to the land of the Gadarenes.
Matthew describes Capernaum as Jesus’ own city.
Jesus left the land of the Gadarenes and crossed by boat to what the text calls his
(idian) city, Capernaum, where he lived (Matthew 4:13) and from whence he had originally crossed the Sea of Galilee (Matthew 8:18). Having lived in the city for twelve months, he had achieved citizenship there and as such it could rightly be called his own city.
During this time Jesus most probably lived in the house of Peter (see Mark 2:1).1
1 And getting into a boat he crossed over and came to his own city.