According to Geoffrey of Monmouth's Historia Regum Britanniae and later works derived from it, Mordred was Arthur's nephew and the brother of Gawain.
The earliest surviving romance the claims that Mordred was Arthur's son is the Prose Lancelot. But in this account Modred's true father is not openly known and most people, including Mordred himself, believe that Mordred is the son of King Loth by King Arthur's sister and full brother to Gawain.
For full information see http://kingarthur.wikia.com/wiki/Mordred .
According to a crossword puzzle by Thomas Joseph dated 3/13/08 in Today's News Herald (Lake havasu city, AZ).
16 down: Arthur's son