Hi! The only story coming to mind is this one?
https://www.mangago.me/read-manga/boukensha_ni_naritai_to_miyako_ni_deteitta_musume_ga_s_rank_ni_natteta/
Maybe you can use this as the base to search?
I searched using "manga where the prince's teacher left him after he lost a leg and adopted a girl in a village and the prince finds him"
This is what Google gave me? Does it sound familiar?
Based on your description, the manga you are likely looking for is "The Abandoned Knight" (also known as The Discarded Knight or The Disabled Prince's Teacher), often found in manhwa/webtoon format. It features a disgraced prince, a teacher who leaves, a lost leg, and the adoption of a girl in a remote village.
Key Details of the Plot:
The Teacher's Departure: The teacher leaves the prince after a devastating betrayal or injury where the prince loses a leg, leaving him in despair.
Life in the Village: The teacher hides in a quiet, rural area, adopting a young girl and living a peaceful, simple life.
The Reunion: The prince, now stronger or seeking revenge/answers, eventually tracks down his former teacher.
Hi! This was one of the earliest stories I’ve read and I don’t know the title but I have a vivid memory of reading it. When I tried to find it, nobody I’ve asked so far had any clues about this to the point where at this point, it might’ve just been a dream. it was about a prince and his teacher who was specifically his swords teacher (I think)? The teacher then decides to leave the prince and go into this remote village elsewhere were he adopts a girl and takes care of her like a daughter. Then, the prince shows up later.