King Arthur had a son named Mordred, however the boy's mother turned out to be the king's half-sister. The magical Merlin prophesied that Mordred would kill King Arthur. So to prevent that and the shame of him having a child with his half-sister, he sent all babies born of nobility on the same day as Mordred out to sea to die.
The Lady of The Lake
The god of the sea spared Mordred's life and he was found by a fisherman. The man and his wife raised Mordred and he enjoyed his childhood running around freely by the sea. One day Nyneve showed up and said that Mordred had to come with her to keep him safe.
Nyneve took Mordred to Lothian where he lived a sad few years with his mother, King Lothe, and two half-brothers. His only happiness came from his dog. Eventually he could no longer bear it so he stole a horse and rode to Camelot to meet his father, King Arthur. His only hope was that the King would recognize him as his son.
The Final Fate
After leaving Camelot on a quest, Mordred ended up going to Avalon to find Nyneve. She tells him to speak with the lady of the lake. Mordred realizes that all he needs is love so he leaves to go find the girl that he met and spent a few days with.
When his love found out that he was Mordred, King Arthur's supposedly evil son, she freaked out and they never spoke again. So then he left and ended up meeting the spirit of Merlin in a raven. He shows him the way that he will kill his father and they way that he will die.
Mordred convinced King Arthur to keep his soul so that he could live happily until his fate finally manifested. So for 10 years Mordred lived happily, when he was 27, he betrayed his father and Arthur killed Mordred. In the end, the King went to Avalon and finally recognized Mordred as his son.