The old Apple ID keeps popping up asking for password.
But cannot access since it was deleted.
Do you really deleted it? or do you set up a new one?
You are sign in here . . . with your Apple ID (?)
Your Apple ID is the personal account you use with all Apple products and services. It includes the email address and password you use to sign in, as well as the contact, payment, and security details that you use with Apple.
You can’t merge multiple Apple ID accounts.
Check your existing Apple ID via your email box, see this Apple article: If you forgot your Apple ID
If you forgot your Apple ID email address or phone number - Apple Support
OR see -> Having trouble signing in?
https://iforgot.apple.com/password/verify/appleid
See this Apple article: If you forgot your Apple ID password
If you forgot your Apple ID password - Apple Support
Then see this Apple article: What to do after you change your Apple ID or password
What to do after you change your Apple ID or password - Apple Support
Read the consequences of deleting an Apple ID -> How to delete your Apple ID account
How to delete your Apple ID account – Apple Support (UK)