Should one resume shaking hands with one's mother's paternal aunt after realizing she is a محرم (unmarriageable kin), especially since one used to shake hands with her previously?

If the intention of your question is that you used to shake hands with non-mahram women, then this is a forbidden act, and we congratulate you on your repentance. Your mother's paternal aunt is in the same position as your paternal aunt; she is one of your mahrams, and it is permissible to shake her hand. There is no sin upon you if you do not shake her hand.