Would entirely depend on what social class the bastards are from. Royalty would likely give them no right to inheritance but allow them to be trained as a knight. Merchant class you're likely looking more at household servant if they're not given away. And peasant class either raised normally or left on someone's doorstep.

If you like you could PM me what you have so far, and I could give you a hand with the little things regarding the world the character is supposed to fit into.