In most usage, this could mean ‘during’. It depends on why you're asking.
Typically, on a quest (or adventure, trip for that matter) is used to emphasize the event of the quest (and more compatible with duration), and the preposition in is most commonly used in contexts like in the quest for (something), which emphasizes the objective of the quest.
In this sentence, without context, we can imagine that the subject is someone like an archeologist who finds what they were looking for (artifacts) or someone playing a video game arranged in quests (and maybe they find some artifacts from a list of things to find, even if they aren't actively pursuing the quest when they find the artefacts). This usage can mean that the artifacts were part of the quest without suggesting that "he" is actively on a quest when he finds them.
In semantic terms, this usage doesn't necessarily entail that the event of finding artifacts happens during his quest. It depends on whether you can generate a contradiction by negating the potential entailment:
He finds some artifacts in his quest.
He finds them during his quest.
If you see a contradiction in the composite:
He finds some artifacts in his quest, but not during his quest.
... then it is an entailment. If not (maybe he finds them after he has stopped the quest), it is not part of the meaning of in.
If so, entailment is only part of (lexical) meaning, and one's conception of a quest might mean it is logically impossible to find something except during a quest; i.e., the entailment is determined by the lexical semantics of quest and logic. It may also depend on whether this is a video game quest (find some items while you are progressing in other ways), a lifelong quest that may never be given up (for the truth, maybe), or a quest for some more immediate goal (like tacos).
Kevin S.
01/04/23
Ethan B.
This is the context: "he sets off in quest of why he is stunted. He finds some artifacts in his quest. He analyzes each one. He then concludes why he is stunted." Does this clarify anything?01/04/23
Kevin S.
01/04/23
Lisa F.
The connector you use "for which" is the subordinator needed in the sentence grammatically. Using "why," even though it can mean "the reason for which," would still not work grammatically01/04/23
Ethan B.
So if he's in quest of "x," and him finding the artifacts is a part of his quest for "x," i would say "on his quest?"01/04/23