Continuously receiving a pop up asking me to sign into my Apple ID and shows my old email id

Wondering if this pop up just started as you got a new Apple device? If you changed Apple IDs years ago, you as such have been using Messages successfully linked to the new Apple ID. The types of things that can cause this kind of issue can sometimes using an older Apple device you haven’t been using, or an app on a device that needs updating but cannot because it is on a device signed in on the new Apple ID. If iCloud is still active with the old Apple ID and a new device pulled from that. If you still have access to the old email and a phone number for verification you may be able to sign in from Settings>Messages - sign in to the new Apple ID.