Hello rusty202,
Thank you for using Apple Support Communities.
We understand that you are trying to delete your email account and add it back with a new password, but it keeps asking for your old password. You can take a look at the following support articles to remove and then add an email account on your iPhone.
If you can’t send or receive emails on your iPhone, iPad, or iPod touch - Apple Support
This section addresses removing your email account:
- On your computer, sign in to your email provider’s website. Make sure that all of your email is there or make sure that your email is saved somewhere other than your iOS device.
- On your iOS device, go to Settings > Mail, then tap Accounts.
- Tap the email account that you want to remove.
- Tap Delete Account.
- Add your account again.
If the steps in this article don't help, contact your email service provider for more information."
Add an email account to your iPhone, iPad, or iPod touch - Apple Support
Best regards.