I’m looking for a word that fits in to this sentence and means dealing with the insignificant:
Twins fans have a knack for fretting over the ______, and this won't relent any time soon.
Minutiae fits your sentence. It is a plural noun
https://www.merriam-webster.com/dictionary/minutiae
“a minute or minor detail —usually used in plural He was bewildered by the contract's minutiae.“
trifle -- n. a thing of little value or importance.
Or trivial, inconsequential, ..
My suggestions would be...
minutiae (noun, plural): The minute/minor details, generally irrelevant or negligible given the current context.
pedantries (noun, plural): The unsolicited, unnecessary, and often distracting interjections made by pedantic people during an argument. These would be your typical "Umm, actually..." sort of assertions; especially so if the statement made fails to contribute meaningfully to the conversation/debate.
semantics (noun, plural): Similar to pedantries, but focused specifically on the choice of words, phrasing, or terminology used in an conversation/debate. If there is no evidence or suspicion of a miscommunication, nitpicking over semantics needlessly distracts from the crux of the issue. (Unless, of course the topic happens to be linguistic or grammatical to begin wtih, or perhaps legally/financially consequential. Try reading a warranty or privacy statement some time, they're a veritable hellscape of semantics.)
As in:
Twins fans have a knack for fretting over a whit, and this won't relent anytime soon.
a whit OED
Without negative: a whit: to a very small extent, a very little. any whit, one whit: to the least amount, in the least degree, at all. every (†each) whit: completely, altogether, thoroughly, quite (in later use almost always with as in comparisons of equality).
For a slightly different tone, how about fretting over ephemera.
According to the Wilipedia, ephemera is derived from the Greek words epi (for) and hemera (a day). It usually means “insignificant” and/or “short-lived”.
Minutae, offered by a previous poster, means “small in space”. Ephemera means “small in time”.
Depending on the subject of the fretting, and whether you’re trying to be serious or ironic, either might be a usable choice.