Unable to login to Apple TV on tv, it’s asks for a password and then a verification code is sent to my phone.

If you have an Apple TV (2nd or 3rd generation) and two-factor authentication for your Apple ID, then you may be asked to type your password followed by the six-digit verification code directly into the password field. Additionally, there is a time limit, after which the code becomes invalid.

Try this: First enter the characters of your password (do not submit yet), then manually request a new verification code, then append that code to the password (no spaces or other separating characters), and then submit. That should help you get passed the time limit.

the verification code comes automatically

I know it does. Still request a new one, after entering the characters of your password, so that the timer gets reset, and you can use the available time for just the code part.