how to delete an apple ID that no longer exists

I have an old apple ID that no longer exists. When I've contacted apple support, I have been told that it no longer exists on their records. The email address associated with the ID has been deleted (I've contacted them to see if they could give me the old email address temporarily, but they cannot) I have a new apple ID, but it defaults to the old one and I see "please enter the password" for this ID every 2-3 minutes that I'm using my phone. I cannot use iCloud services or apple pay. I cannot log out of this ID without putting in a password. I've tried using the password for the new apple ID, but it doesn't work either. This is so frustrating. Is there any way to delete this and use my new ID?