Hi there Shadow5199_6420,
We understand you have a question about signing in to your iPod touch with your Apple ID with two-factor authentication enabled, and we'd like to share a resource that can help.
Check it out here: Two-factor authentication for Apple ID
Specifically, the section below may help:
"What if I use two-factor authentication on a device running older software?
If you use two-factor authentication with devices running older OS versions—like an Apple TV (2nd or 3rd generation)—you might be asked to add your six-digit verification code to the end of your password when signing in. Get your verification code from a trusted device running iOS 9 and later or OS X El Capitan and later, or have it sent to your trusted phone number. Then type your password followed by the six-digit verification code directly into the password field."
Cheers!