How do I remove an old notification email from my Apple Account?

I have been trying to remove an old Notification email in my Apple account. When I try to remove it, it tells me to continue on another device (go to Settings, Apple Account), but when I do so nothing happens. It tells me it is sending a code to my email address, but I receive nothing there. This is a continuous loop. It repeats the instructions, but nothing happens and it will not allow me to delete the Notification email. I no longer have access to that email and need to delete it. When I login to my account on one of my other devices, this does not show up. The option for Notification email is only on the online version of my account, not my other devices. Please help.

[Re-Titled by Moderator]