Apple ID not found and cannot create new ID

I tried to reset password and got response that the Apple ID does not exist. Then I attempted to create a new Apple ID and got a response that the user ID (email name) is already in use.

In other words, the email address already exists when I try to create a new Apple ID, but when I try to reset the password, the reply says that the Apple ID doesn't exist.

Is there a way to reset this Apple ID so that I can log in without creating a new email account?