How to manage AOL mail on iPhone?

Not sure what you are asking.

Unless you have previously moved an email message manually to Archive, there is nothing in the Archive folder. For example, if you are looking for a deleted email, it won't be in Archive unless you previously and manually moved to the Archive folder.

Open the AOL app

Tap on New Mail in the lower left corner of the screen

Tap on New Mail again, and then tap on Archive to view the contents of the Archive folder

The best way to manage AOL mail, in my opinion, is by using the AOL app. You can download the AOL app from the App Store app. The AOL app will manage your AOL mail and more.

Axel F.