Apple TV: Account verification nuisance
Depending on what specific verification item is problematic, you might need to reset the Apple TV and make sure your Apple ID and date/time setting work before loading any third party apps or logging into other accounts. 

There is a chance you could use Xcode to look over the AppleTV logs and determine what app is triggering the requests, but it might be faster to wipe and verify it’s not software corruption or storage issue.