I think this is already one of the core features of osTicket.
1. Log in to http://yoursupportsite.com/scp(http://yoursupportsite.com/scp) (of course, replacing yoursupportsite.com with wherever you have hosted your instance of osTicket)
2. In the upper-right corner, choose "Admin Panel"
3. Select the "Emails tab"
Now you should see a list of email accounts that are associated with osTicket, including the priority that will be assigned to tickets created by receiving at that account.
Click on the email to type your POP or IMAP and SMTP information in to it, and make sure you have set up the cron jobs as described in the setup documentation. I haven't looked at the source code for the cron.php script, but I bet it is the script responsible for kicking off checking the mailboxes for those email addresses every minute (or however often you configure cron to do so).
Besides setting cron to run osTicket's cron.php script every minute (or whatever you choose), you should set the "Fetch Frequency" under the setting for each email address.
So now you can have support@yourdomain.com, help@yourdomain.com, billing@yourdomain.com, business@yourdomain.com, residential@yourdomain.com, emergency@yourdomain.com, etc. and they can all have specific priorities assigned to them based on what email address received them.
I have mine set up with Google hosted email (google for your domain, I think they call it) and it works perfectly.