kjamal
Deleting a Ticket permanently deletes the Ticket and any record of it. This means if the email is refetched it will create a new Ticket as the system doesn’t have any record of it. That box you are referencing only applies to non-deleted Tickets with that specific Status.
What you really need to do is login to the mailbox itself, clean the inbox (or configured fetch folder) of any old and processed mail, go to your Remote Mailbox tab for your email in osTicket, set the Post Fetch to Archive, add a folder, and Save Changes. Now when mail is fetched it will be moved out of the fetch folder into a separate folder where osTicket will never process it again (unless it’s moved back manually).
Cheers.