Looking for a fantasy manga

About a boy who gets kicked out of his noble house because he’s “useless”. I can’t remember if he’s reincarnated or not. He registers with the adventurer’s guild. The guild receptionist is a a guy with a scar on his face and he’s missing a lower leg because he defended the city. He takes the boy under his wing. The boy becomes a magic teacher for one of the princesses and gets adopted by the guild receptionist. He heals his new father’s leg. He also protects a baby dragon.