In the medieval stories of King Arthur, Sir Morien was the son of a British (Christian) knight and a Moorish (and thus presumably Muslim) princess. His parents met when his father visited his mother's country, the two fell in love, and then his father returned back to his home country without marrying Morien's mother.
Within the story itself, Sir Morien ventured forth on a quest to his father's country with the aim of finding his father and convincing him to return back to his mother so that they could be wed, and Sir Morien himself would eventually be able to inherit the crown of his mother's kingdom as a now-legitimate child. In the end, after some questing and some duels with Arthur's knights, he finds his father and convinces him to return to wed his mother. Happy endings for everybody.
Of course, this story was written by someone in medieval Europe who would have had no idea of how the Islamic culture or legal system worked.
What would the legal situation of someone in Morien's circumstances be, under Islamic law and custom? Would he be potentially able to inherit the rulership his mother's kingdom, with or without his father returning to marry his mother? Would his father returning to marry his mother actually change anything?