noun which may take the genitive case particle 'no', noun
with a story; with a shady past; with complicated circumstances
Describes a person, object, or situation that has some notable, often questionable or difficult-to-explain background. The nuance ranges from merely interesting to clearly dubious, depending on context.
あの骨董品はいわく付きらしい。
That antique seems to have a story behind it.
彼はいわく付きの過去を持つ人物だ。
He is a person with a shady past.
Kanji spelling using 曰く; less common but still seen.
Compound of 曰く (iwaku, 'story, reason') + 付き (tsuki, 'attached, with'). The exact historical derivation is straightforward; the word has been used since at least the Edo period.