How to prevent deleted emails from reappearing in Apple Mail on iMac?

iMac Sequoia 15.4.1

email service provider: aol

mail application is Apple Mail

Deleted emails reappear in inbox with a minute of their deletion. Have had this problem multiple times over the years with multiple iMacs. Thought it had been solved but has reoccurred yet again.

[Re-Titled by Moderator]

Original Title: deleted emails reappear