How do I make your new Apple ID permanent on your iPod Touch 5g???

So every time I go into my Settings, press on "iTunes & App Store" it's fine and it shows that I'm signed into the new Apple ID that I want. Then I press on "iCloud" and "Game Center" but it has my old Apple ID. When I go into "iCloud" a thing pops up asking me to type in my password but it's asking me to type in my password for my old ID. Every time I press "cancel" it pops up 2 seconds later asking me to type in my password. When I type in my password it pops up every 2 seconds like three more times then tells me that my password must be wrong!!! I need help because my iPod can't function that well!!! I need to make it so my new Apple ID is permanetly in the iPod. I can't look at my storage, go into iCloud in the settings without is asking for my password, I can even update my apps!! So could somebody help me please??? By the way, it's not the password, it's the ID, I need to change the ID from my old one to the one that I want to permanately be in my iPod!!! Thanks!!