Deleted emails keep reappearing

You need to go to Settings>Mail>Accounts>tap on the account in question. Tap the account again, you will get the first page, then tap Advanced. Then you will see the setting "Move Discarded Messages Into:" You can select either Deleted Mailbox or Archive.

Are you saying that you have deleted the mail in your deleted mail box, and then when you go back there, the mail is appearing again? Is the mail account set to delete mail or to archive mail? There is a difference.

You're welcome.