Error "Could Not Sign In" Server Connection issues on my iPod Touch 4th Gen

The most recent version of iOS that your iPod can use (if it's a 4th generation iPod Touch) is iOS 6.1.6, but access to the iTunes Store from the iPod now requires iOS 10.0 or later.

However, you should not need to sign into the iPod in order to set it up. Instead, use iTunes (the desktop programme) to set up the iPod and copy media (music probably) to it from your iTunes Library. You can buy music from the iTunes Store via iTunes (again, from the desktop programme) or Amazon, Bandcamp etc. as well as copying from CD into iTunes. If you purchase music from other stores (i.e. Amazon etc.), you download it to your computer and then add it to your iTunes Library. Finally, you copy that library to your iPod.

If you don't know how to perform any of the steps above, post back with specific questions and we can probably help you.

You will need to uninstall the Apple Devices, Apple Music and Apple TV apps from your computer. Once you do that, you should be bale to use iTunes as you did before.

See the reply from turingtest2 in your other post, Transferring music from iTunes to older i… - Apple Community, that effectively says the same as I did. (He's the expert on this, not me!)