Correct option is A
The most appropriate option to replace the highlighted word with the adverb of frequency is (a) never admitted.
An adverb of frequency is an adverb that describes how often an action occurs. Examples include:
Always, Usually, Often, Sometimes, Rarely, Seldom, Hardly ever, Never.
The sentence talks about someone not admitting something, which means they did not do it at any point in time.
Therefore, "never admitted" is the correct adverb of frequency to replace the highlighted word.