Emails keep returning after deletion

That usually points to a sync issue with the mail account rather than the iPhone itself.

I’d check whether the messages stay deleted if you remove them directly from the provider’s webmail site. If they come back there too, the issue is with the mail server/account.

If they delete correctly on webmail but keep returning only on the iPhone, go to Settings > Apps > Mail > Mail Accounts, select the account, and make sure Mail is still syncing normally.

Also check whether those messages are being moved to Archive instead of Trash, since some accounts use Archive as the default action.

If you tell us which email provider you use, such as Gmail, Outlook, Yahoo, or iCloud Mail, that would help narrow it down.