How to change my apple ID on iPhone?

I actually use to have a different account on my phone and changed it a while back, but just recently I tried to update Something in apple store but it asked for the other accounts password… It's never done this before and I did everything I could think of:
Turn of phone/turn back on
Re login
That's about it… Well It says that I'm logged into the right account, but when I try the update it asks for the other accounts password…

The account that you originally download the app with will be tied to that app on your phone forever so you should try re-downloading your old apps that you used that account for.

Or you could just keep using the old account password for those apps.