His wrongdoing was completely exposed, but not once he apologised for his actions

The sentence aims to draw a comparison between the admission of wrongdoing and the lack of an apology. Although the phrase "not once" is intended to highlight the fact that he never expressed regret, the structure that follows it is incorrect. This is an example of inversion for emphasis, a construction in which a negative adverbial such as "not once" should be followed by an auxiliary verb before the subject. The correct inversion structure is  “Not once did + subject + V1” (V1 refers to the present tense form of the verb)

The correct choice is therefore option A .