We don't know much of anything about Jhin's childhood and general past, other than the fact that Rioter's confirmed the following in his Q&A thread:
-He had a father.
-His father once ran a struggling dojo that specialized in chi blade techniques, which eventually closed shop when it couldn't compete with the rising popularity of wuju school dojos.
-Jhin despises Yi in particular due to the fact that Yi's dojo was the specific wuju dojo that his father directly competed with, and thus the one that drove his family out of business.
-Jhin was actually an arcane prodigy as a child, and used his chi life essence to transform his victims into "artwork." Like making flowers sprout out of the bodies, or painting the bodies gold.
-Jhin used these chi-blade techniques on his victims in his serial-killing days.
-Jhin was in Tuula prison when the first Noxian invasion occurred.
-Jhin collected trophies of his kills. What those trophies are and what he did with them, we don't yet know.
-Rioters strongly implied that we'll get a lore event where Shen will try to recapture Jhin through an undercover investigation, discovering the mystery behind his past and how or why he became a serial killer. Something like that.
Assuming that's everything, then this is all that we know.