Apple ID change on iPhone 6s

Consider signing out of each and every device that uses the Apple ID.

What to do after you change your Apple ID email address or password - Apple Support

Try to sign out of the old Apple ID on all of your devices. After doing this, sign back into your new Apple ID on each device.

Make sure you pay attention to the questions that will be asked when signing out of iCloud, depending on your answer, it could result in data loss.

Choose to delete your account altogether by taping signing out:

If you're no longer using the email address associated with your Apple ID, you can change the email address that you use as your Apple ID, then use the steps below to update it in the services on your device. If you forgot your Apple ID, there are a few ways to find it.

iCloud

1. Tap Settings > iCloud on your iOS device. If you see the option to sign in, you can change your Apple ID now.
2. Scroll down and tap Sign Out.
   
3. Tap Sign Out again to confirm. After you sign out of iCloud, you might not be able to access some of your data that's stored in iCloud until you sign in again. If you're part of a family, you need to sign back in to use Family Sharing.
4. Choose Keep on My iPhone or Delete from My iPhone when you're asked what you want to do with your iCloud data.
5. Enter your password to sign out.
6. Go to Settings > iCloud and enter your Apple ID and password.
7. Tap Sign In.

If you updated your Apple ID email address and your device repeatedly asks for the password to your previous Apple ID, you can temporarily change your Apple ID to sign in.

Also check on how to Change your Apple ID - Apple Support