I changed my Apple ID but my old email still shows up on my ipad 9.3.5. How do I fix this?

This support page describes how you can create a new AppleID account:

How to create a new Apple ID - Apple Support

Before you do so, perhaps consider that an AppleID account is intended to be used for life with all of your devices. If you need to change the primary email address that identifies your account, or your secondary (recovery) email addresses or trusted telephone numbers, you simply need to update your AppleID account as necessary.

Change your Apple ID - Apple Support

Change your Apple ID password - Apple Support

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

Change, add, or remove Apple ID payment methods - Apple Support

Few of us will have the luxury of forever keeping the same email addresses or telephone numbers - sometimes these needing to be changed for a variety of reasons. However, updating our AppleID account, maintaining access to our data and purchases, is easy and relatively straightforward - accommodating life’s many changes as they occur. Using a completely different AppleID account can introduce many complications and issues, not limited to losing access to paid Apps, subscriptions and services - these being forever tied to the AppleID account from which they were purchased.

If you do wish to change and use an entirely different AppleID, first ensure that you have disabled the Activation Lock that will otherwise cause difficulties in the future. You can disable the Activation Lock by disabling the Find My service from iPad/iPhone settings before trying to use a different AppleID account:

Settings > [Your Name / AppleID] > Find My > Find My iPad - set to OFF

Having disabled the Activation lock, you can now sign-out from your old AppleID:

Settings > [Your Name / AppleID] > Sign Out

Presumably you’ll want to keep any iCloud data that is locally stored on your iPad. If so, accept the opportunity to keep a local copy of your data (e.g., Calendar, Contacts, Notes, Keychain Passwords etc.) - as otherwise this data will be wiped from your iPad as you sign-out from iCloud. 

Also ensure that you have signed-out from Messages and FaceTime:

• Settings > Messages > Send and Receive > [AppleID] - scroll to the bottom where you will find your signed-in AppleID highlighted in blue text; tap and select Sign Out

• Settings > FaceTime > [AppleID] - again, scroll down the page to find your signed-in AppleID highlighted in blue text; tap and select Sign Out

After signing out, a restart of your iPad/iPhone is recommended:

Restart your iPad - Apple Support

Force restart iPhone - Apple Support

After restarting, you can sign-in to your new AppleID account from iPad settings - and also sign-in to Messages and FaceTime if necessary. Any iCloud data that you saved to your device during the previous sign-out will be merged with your new AppleID account.