noun which may take the genitive case particle 'no'
some; a small amount
Used to indicate an indefinite but small quantity or degree; often followed by a noun with の or used adverbially.
幾ばくかのお金を寄付した。
I donated a small amount of money.
彼の話には幾ばくかの真実がある。
There is some truth in his story.
Combination of 幾 (いく, 'how many') + ばく (an old counter/quantity word) + か (question particle). The exact derivation of ばく is uncertain, but the whole expression has been used since classical Japanese to mean 'some amount'.