Mark 1:21,29 — „Simon and Andrew lived in Capernaum."
John 1:44 — „Andrew and Peter were from the same city as Philip, which was Bethsaida"
This apparent contradiction comes for the most part from not reading these passages carefully. If we read these carefully and note what is said in each passage, the problem is quickly solved.
John 1:44 declares that Philip was from Bethsaida, the city of Simon Peter and Andrew. We learn that Philip came from this city; and when it says that this was "the city of Andrew and Peter" it simply means that this was the city where they originally came from.
In Mark 1:21 and 29 it says, "And they went into Capernaum …" and later then, "And forthwith, when they were come out of the synagogue, they entered into the house of Simon and Andrew …" These verses show that Simon and Peter were living in Capernaum at the time of this record.
Simon Peter and his brother Andrew were originally from Bethsaida, and they obviously had grown up there. At some later time, perhaps due to their profession (being fishermen at the sea of Genezareth) they had seemingly moved to Capernaum. In mark, we also learn that Peter now was married, because Jesus healed Simon Peter's mother in law when he came to Peter's and Andrew's home. As is the case in our day and time, people in biblical times didn't necessarily live their whole live in the same location either but moved for various reasons to other cities as well. If we recognize these facts, the apparent contradiction is solved quickly and without much difficulty.