If iCloud asks for the password to your previous Apple ID
Your iPhone, iPad, or iPod touch might ask for the password to your previous Apple ID when you sign out of iCloud. If you can’t sign out of iCloud because the Apple ID email address shown is one you no longer use, follow these steps.
Update your device to iOS 10
Update your iPhone, iPad, or iPod touch to the latest version of iOS 10. Then try signing out of iCloud again.
If you can't update to iOS 10
If you can't update your device to iOS 10 and you're still asked for your previous Apple ID, you can temporarily change your Apple ID.
If you're trying to restore from a backup and Setup Assistant asks you for the password to your previous Apple ID, tap Skip. After you complete the Setup Assistant, you can sign in using Settings.
Change your Apple ID temporarily
Use these steps to change your Apple ID temporarily:
Sign in to your Apple ID account page.
Click Edit in the Account section, then click Change Email Address.
Change your Apple ID to the email address that iCloud is asking you to sign in with.
Sign out of your account page.
Then sign out of iCloud on your iPhone, iPad, or iPod touch:
Tap Settings > iCloud on your iOS device.
Scroll down and tap Sign Out, then tap Sign Out to confirm. If you're using iOS 7 or earlier, tap Delete Account, then tap Delete to confirm.
Tap Keep on My [Device] or Delete from My [Device], and enter the password for your Apple ID. Your data remains in iCloud, and is updated on your device when you sign in to iCloud again.
If you're signed in on more than one device with this Apple ID, repeat steps 1-3 on each device.
Go to your Apple ID account page, and sign in again.
Change your Apple ID to the email address that you want to use. You'll need to verify the email address.
Tap Settings > iCloud on your iOS device, and sign in with your new Apple ID.
If these steps don’t work, change your Apple ID temporarily again. Then sign back in to your Apple ID account page to make sure that your Apple ID was changed.
Whenever you change your Apple ID, remember to update the features and services that you use with Apple ID, so that each one is using your updated Apple ID.
Learn more
If you don't need to sign out of your previous Apple ID but want to sign out of someone else's Apple ID on your device, follow these steps to turn off Find My iPhone Activation Lock.