Phone Recognized Wrong Apple ID

Can someone help me with a problem I've had for three years?

I have an old Apple ID that is a former work email I no longer have access to. I have created a new Apple ID with a new gmail address and logged in, but my phone still asks me to sign in with the password for the old Apple ID dozens of times each day.

It says "Sign in to iCloud... Enter the password for your Apple ID (old, wrong email address)" and all I can do is select Cancel. It goes away for a few minutes or an hour or so, then pops up again.

When I go to Settings and click on my name, when I try to click "Name, Phone Numbers, and Email" is only pops up the same box asking me for my old, wrong Apple ID.

It's very frustrating. I have shown it to workers at two different Verizon stores, and had a half hour conversation with a tech on the phone with Apple, and nobody can figure out how to fix the problem.