What part of speech is the word aha?

It is an interjection.

It is used as an exclamation of triumph, mockery, contempt, irony, surprise, or other emotional utterance. Note that when aha is used in a sentence, it typically appear in dialog, and then is often set apart from the sentence by an exclamation point or comma.

Example: If Archimedes had exclaimed "Aha!" rather than "Eureka!", his famous outburst might not have been so notable.