itunes sign in on ipod

I have a 64GB iPod Touch, model MC547LL/A running s/w version 6.1.6 (10B500). I cannot sign in to iTunes. I enter my ID and password but it tells me they are incorrect though I am able to successfully sign in on my iPad Mini and on my iPhone 5S and my MacBook Pro using the same ID and password. A 6 digit verification code goes out to the other devices and I am instructed to re-enter my password with the verification code appended to it. I do this and it simply comes back password incorrect, try again and the process repeats. I have tried multiple time, ensuring that I enter the ID and the password with the appended verification correctly but still not able to sign in to iTunes on the iPod.