If you subscribed through Apple it's possible that you had Apple ID protection selected at the time of registration in which your registration email was replaced with a random email address created by Apple. You then will need to use that email address to log in. That's the private email that Apple generates when you use the Sign in with Apple feature.

Here are a few ways to help recover your subscription by re-linking the purchase.:

1. Let's try deleting and reinstalling the app. Now, when you are in the app when it eventually asks you to sign up (pay) again, just hit the Restore Previous In-app Purchase link. This will then switch your subscription to use the subscription that you have purchased/initiated.

 
2. Restore Purchases: How to Restore Apple App Purchases 
  • Firstly double check that you are logged into the correct iTunes account and you have purchased a magazine under that Apple ID.
  • In the app go to Profile > Restore iTunes Purchases.
  • Tap Restore.
3. Tap the black Apple Login button:
  • To log back in with this email, just tap the black Login with Apple button. No need to type anything in, just hit that button