Since the iOS 10 update, the way to update new email password in the Settings app has changed.
How do I change my email password on iPhone & iPad?
On iOS 9 and earlier, you can change your email password in the Mail settings by doing it this way:
1. Go to Settings → Mail, Contacts, Calendars → Your Mail Account → Account.
2. Tap the Password field, clear it and then enter your new password. Tap Done to finish.
3. You may also need to go to “Outgoing Mail Server Setting” → Primary Server → Password and update your password here.
If your device is running iOS 10 or later, this feature has changed a bit. Mail settings are now separated from Contacts and Calendar, you can access it in “Accounts & Passwords”.
To change the email password, go to Settings → Accounts & Passwords→ Your Mail Account → Account. Now tap on the “Password” field and update your new password.
If you cannot see the Password field there, it means your email provider no longer allows you to change your password from within the Settings app on iPhone. In this case, you may need to go to your email provider’s homepage using your web browser, sign into your account, then change your password by following the provider’s instructions.
For Google Mail: https://mail.google.com
For Yahoo Mail: https://mail.yahoo.com
After you update your password in a browser or on other devices, if your email still gets to your iPhone or iPad, then you’re all set. Many popular email providers that interact on an account level with iOS will update your info automatically to remain the communication.
If your iPhone or iPad cannot communicate with the email server. Go to Settings → Accounts & Passwords→ Your Mail Account. It may provide you an option to re-enter the password, like in the screenshot below. Just type in the new password and you’re good to go.
If the option doesn’t appear, then manually remove your email account from your iPhone by selecting “Delete Account” from the Accounts section. Then you can re-add it with the new correct password.