Hi arnthor2,
Thanks for participating in the Apple Support Communities. We understand that you're unable to enter the six-digit verification code for two-factor authentication on your Apple TV 3rd generation, so we'd like to share some information with you. When you get the verification code from a trusted device or trusted phone number, type your password followed by the six-digit verification code directly into the password field. Learn more from the, 'What if I use two-factor authentication on a device running older software?' section of this article: Two-factor authentication for Apple ID.
Take care.