The pattern [i-adj]くもなんともない is an emphatic way of saying that something is "not at all [adjective]" or "not [adjective] in the slightest". It strongly denies a quality or feeling, often dismissively. The speaker is asserting that the adjective in question absolutely does not apply.
To form it, take an i-adjective, change it to its く-form (the adverbial form), and attach もなんともない. The literal sense is something like "not [adjective], not anything" – a double negation that reinforces the denial.
This expression carries a strong, dismissive tone. It is used when someone else has suggested or implied that something is the case, and the speaker wants to firmly deny it. It can sound blunt or even defiant.
It can also be used to express that something fails to affect the speaker emotionally or physically:
~くもない is a milder version meaning "not even [adjective]" but lacks the extra emphatic punch of もなんともない.
全然~くない ("not at all") is more neutral in tone, while ~くもなんともない sounds more emotional and dismissive.
Since ない at the end is a regular i-adjective, it can be conjugated into past tense (なかった) or polite forms (ないです / ありません).