ITUNES APPLE TV LOG IN

If you have an Apple account then you already have an Apple ID, which is what you already used to log in. There isn't a separate iTunes account. It sounds like there may be an issue with Prime. Which model Apple TV do you have?

Identify your Apple TV model - Apple Support

no appleID/itunes account/ icloud login

are not something that cost

https://support.apple.com/lv-lv/HT204316

https://appleid.apple.com/account#!&page=create

Ok. So that screenshot provides more information, which changes things. As this is a new account the message is telling you that you need to log in on one of those devices first. Then you can sign in normally here.

If it was purchased from Apple or an authorized reseller then it would be one of the current models, the HD or 4K. Make sure the software is up to date (TVOS 13.3.1).

You can try signing out and back in with your Apple ID. If that doesn't work then force quit the app (double tap the home button on the remote to bring up the app switcher, swipe up) and/or delete it and reinstall (press and hold down on remote touch pad until icon jiggles, press play/pause to bring up options and date, download from app store).

If the issue still persists then you should reach out to Amazon.