App Store asking for my AOL password

Do you mean it is asking for the Apple Account password, which was using an AOL email address?

If you created an Apple Account using the AOL email address and downloaded an app to a device previously, then anytime that app wants to update, it will require the Password to the account that downloaded it, no matter what Apple Account you have currently signed into your device. Apps are linked to the Apple Account that downloaded them.

Also on your device, what account do you have signed into Media & Purchases currently at Settings > [name on top] > Media & Purchases. Please don't post that email address, I am more interested if this is the AOL email address you are referring to.

If you can post a screenshot of what you are seeing with the email address redacted, that may be helpful too.

You may want to check whether the password request is really from Apple:

Eg: Identify legitimate emails from the App Store or iTunes Store - Apple Support

or

Recognize and avoid social engineering schemes including phishing messages, phony support calls, and other scams - Apple Support