https://www.mangago.zone/read-manga/reaper_of_the_drifting_moon/
There's this webtoon not sure if it's what you're looking for but there's some similarities..MC and other children are kidnapped and trained to be assassins of some sort underground.. He also fell down and gained some type of martial arts if I remember correctly. But I don't think they mentioned anything about a father.. I dropped this long ago because I was annoyed with MC lol
If you're interested to see some other Murim webtoons
Murim List
https://www.mangago.zone/home/mangalist/2097563/
Happy Reading!
(๑•ㅂ•)و✧
Oh sadly it's not this, and ye I dropped it too lol. Also thanks for the list!
Oke looked for it myself, it's this https://www.mangago.zone/read-manga/the_sword_of_glory/
It's set in murim, mcs are a father and his son. They got separated, the son got kidnapped I think and got sent somewhere tho I forgot what kinda place it is but there's a bunch of other kids too. The son fell down somewhere there and ended up in this cave where he had to survive and found some martial arts technique. As for the father, he has been desperately looking for him but he ended up getting amnesia which frustrated me so much so I dropped it but now im wondering what happened to em