How can I remove an old email address from my apple id? Even tho I've had a new one for 3 yrs, the old one keeps showing up demanding passwords, etc.

Have you signed out of the old address in System Preferences/iCloud (Apple ID for Catalina) and Settings/Your Name/iCloud? If you go to System Preferences/iCloud (Apple ID for Catalina), what ID shows there?

Where is the old ID showing up? Is the requested address a different Apple ID or a previous address used with your existing ID?