A new email from a user creates a ticket but it gets merged with an old ticket thread -- even though the user says they sent a fresh email.

Check the View Email Headers option on the merged thread entry (dropdown arrow > View Email Headers). If the email contains In-Reply-To or References headers matching a prior thread Message-ID, osTicket correctly identified it as a reply. Users sometimes hit 'Reply' instead of composing new. There is no setting to disable In-Reply-To thread matching.