Out of the blue, I receive a message from Apple asking for my Apple ID password. I put it in and continue using my iPad Air 2.

It is SCAM! Apple never ask you out of the blue for your Apple ID password. Check this link: https://support.apple.com/en-us/HT204145

I am having the same issue. I am constantly being prompted throughout the day to "Update Apple ID Settings. Some account services will not be available until you sign in again."

Then it asks me for the iPad password

This is within my iPad settings so contrary to what @BORg529 said this is not a hack.

Unless you were in beta program, and never delete it right. Nobody cannot see what you mean from the photos you provided. Also, if you do provide better photos, do not post personal information in public forums, very dangerous.

This does not appear to be a scan because I'm experiencing the same thing on my iMac that has a partition specifically for Catalina. The preference pane is brought up so that I can log in to my Apple ID. I complete that task. Then I'm ask for my machine ID. I have experienced this repeatedly. And I have reinstalled Catalina.

Agree . . . this is NOT a hack!

Can you post a picture of the screen you're seeing?

Have you restored your device recently?

~Lyssa

I am having the same problem on my air 2. It started a few weeks ago. Did you ever find a solution to this problem? I would be thankful for any solution.

contact apple, I was instructed to forward that email to them and it was spam

How do you stop applied requests? I’ve tried a lot of things, it’s driving me nuts!!!!