I have an iPod Touch running iOS 5.1.1 and i am trying to redownload an app (Overdrive) for it. When I try to log into the App Store I am asked for an authentication code. The authentication code pops up on my iPhone, but there is no place to enter i

Big fail on apples part. They need to say that's how you do it but no where do they say that. Spent an hour this morning trying to figure that out.

Answer is enter your password followed by verification code that was sent to your phone. (No spaces)

Actually they do say what to do. You sound like me when something doesn't work but the instructions actually do say to enter your password and the verification code in the password area. Unfortunately, it only seems obvious after you struggle with it for a while and then it finally works. The convenience of the digital age can be quite frustrating to an old guy like me.

Oh My goodness,,, finally!!!!!!!! thank you

Figured it out. In the password slot (only space available on the ipod) type in both your password and the authentication code (no spaces), and your password should get recognized.

It sounds like you have two factor authorization setup for your APple ID. However, to use two factor on an iOS device the device need iOS 9 or later

Trusted devices

A trusted device is an iPhone, iPad, iPod touch, or Mac using iOS 9 or OS X El Capitan that you've already signed in to using two-factor authentication. It’s a device we know is yours and that can be used to verify your identity by displaying a verification code from Apple when you sign in on a different device or browser.

From:

Two-factor authentication for Apple ID - Apple Support

So what should I do. Down load ios 9 to my ipod? How do I do that?

Delete the two point verification, and then add the ipod as a device to my list?