Unread emails can hide in folders other than the Inbox, if they got moved before opening. If you tap the Mailboxes button top right abover list), then the account name (second half of mailbox list), you will see all the folders in that account. Andy folders with unread email in them should have a number to the right.
If you have an IMAP or Exchange account (Gmail, Hotmail, Yahoo, iCloud and some others) then it would probably be easier to delete and re-add the account than to hunt down and mark as read all the emails.
In a POP3 account, you should only have Sent, Trash, and maybe a Drafts folder. These will be local, and you should be able to Edit and Delete All for the Trash folder; and hopefully clear the issue.