Most owners of Apple hardware have different generations of equipment in use. And because the company's equipment can last a long time, you can end up with some old equipment – like an old Apple TV or Mac used to serve video or what have you.
Apple has shifted aggressively to require two-factor authentication (2FA) with Apple ID accounts as a way to discourage account hijacking. This is admirable, although it has some unfortunate side effects for people who have multiple Apple IDs for historical or other purposes. (I wrote a couple of years ago about using multiple macOS accounts and other tricks to manage it.)
But 2FA and outdated versions of Apple TV, iOS and macOS cannot be mixed. You try to sign in to these devices with your Apple ID, and code pop-ups can appear on other devices, but there is no way to put it into the device you are trying to log into.
Fortunately, there is a simple solution:
Log in with your Apple ID and password as normal.
Get the six-digit verification code from one of your trusted devices associated with Apple ID.
Back to the original device, login again, but add this six-digit code at the end of the password. (Do not place a space or anything else between the password or the code.)
You can also generate a verification code manually:
On iOS, open Settings> [your account]> Password and Security and press then on Retrieve verification code.
In macOS, go to the iCloud Preferences pane, click the Security tab, and then click Get Verification Code.
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