Hi sharonfromalbstr,
We appreciate you reaching out to us. We understand that you are experiencing issues you are getting a pop-up on your phone for an Apple ID verification code for your older model Apple TV, but the there is no option on your Apple TV for you to enter the code.
We’d like to gather additional details that may help us be in a better position to assist you.
Does it seem like the verification code is for the two-factor authentication for Apple ID?
Based on your post, it seems like you are using an Apple TV 3, is that correct?
If you answer yes to both questions, your Apple TV 3 does not meet the system requirements for the two-factor authentication for Apple ID.
Two-factor authentication for Apple ID
Take care!