Initial emails sent to the mailbox currently create a new ticket, however, if recipients in the email reply (which includes the mailbox) it SHOULD NOT create a new ticket in the Project ticket
What route are you using for email?
Is it a standard Jira built-in email handler? If so, you should probably swap from a "create issue handler" to a "create or comment handler". The create or comment handler will check the email subject for issue keys and convert the email to a comment on the email rather than create a new issue each time someone replies.
JETI is a powerful email tool, a lot more clever than the default Jira email handlers. I have not used it for a while, so I can't really help you configure it, but I do know it's been able to identify incoming emails as comments based on a load of things in the email, not just having the issue key in the subject.
Look for "processing strategy" in the docs, if memory serves.
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