Hi there Areyes4apple,
If deleting an email in the Mail app does not delete it from the AOL mailbox, let's first ensure you are following the steps outlined here to delete these emails: Delete emails on your iPhone or iPad
If you are following those steps and this continues, next check that you added the AOL email account to your iPhone using the recommendations of this article: Add an email account to your iPhone, iPad, or iPod touch
If this persists after reviewing those, let us know if you are able to send and receive emails without issue in the Mail app on your iPhone. That will allow us to isolate whether the Mail app or the email account is responsible for this behavior.
Cheers!