Locked out of inactive Apple ID account

My iPhone 6 is repeatedly asking me for the password to an apple ID that is no longer active. Every 60 seconds or so there is a pop up asking me to go to setting and enter the password, but when I get there and put the old password in, it won't recognize or accept it. When I go to find the forgotten password it tells me that there is not an account with the email address it asks for.

I've tried syncing it with my Macbook but that did not seem to work.

For now I've just been hitting 'Not Now' on the pop up but it's very frustrating when I am trying to look something up or send a text.