AppleTV

If it turns out that 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 code would be entered on whatever device is trying to Airplay to it. If you are not trying to airplay to the Apple TV, then simply click the menu button to exit out of the code screen.

A First generation Apple TV is a silver and white slab from 2007, and is no longer supported by Apple and does not support Airplay at all:

Link-> Identify your Apple TV model - Apple Support