Q: Can't sign it to iTunes on iPhone

Hi. I own an iPhone 5s that is currently running OS 10.0.2. I also own a Mac Mini that is running OS Sierra. In the process of upgrading to Sierra, I changed the password of my Apple ID.

The problem I'm having is that iTunes on my phone will not accept my new password. So I can't run the App store on the phone to update apps. I just tried to update all apps on my iPhone using iTunes on my Mac but there were some errors and a few apps didn't get updated. Normally when this happens, I then update the apps using the App Store app on my phone. But I can't do it now because iTunes on my phone is not accepting my password.

Something strange is going on because that same password is working just fine on my Mac. I sign into iTunes on my Mac with the same Apple ID and password that is giving me errors on the phone. I'm also able to log into the Mac App store and this website, all which use the same username and password. So I have no idea why iTunes on my phone is not accepting the new password.

Can anyone tell me how to fix this problem? Thanks.