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.
https://sanascans.com/series/a-second-life-at-the-edge-of-the-world/chapter-1
https://sanascans.com/series/i-was-isekai'd-with-my-apartmentnow-i'm-a-scorned-noble-lady-living-free./chapter-1