Well alright, apologies for the sarcasm, apparently I'm in a bit of pain and it limits my patience.
Have you verified that the IMAP account is accessible by the server? This might help:
https://support.plesk.com/hc/en-us/articles/213961665-How-to-verify-that-SSL-for-IMAP-POP3-SMTP-works-and-the-proper-certificate-is-installed-
Then check the osTicket admin page for the server system settings, it should show ticks for all the modules and settings etc, navigate to "Admin panel" -> Dashboard -> Information, which has URL /scp/system.php
I use this on Ubuntu myself, so it definitely works, but if you don't have the right modules installed, it's not going to work. You'll need php extension imap for what your trying to do.
Next verify your IMAP settings, for instance working Gmail settings are like this
"Admin panel" -> Emails -> Your Account:
Under: Fetching Email via IMAP or POP
Status Enable
Hostname imap.gmail.com
Port Number 993
Mail Box Protocol IMAP+SSL
But it depends on your email host etc what those are. For Gmail you use the full email address as the username and set the password.
If you use 2fa for the account, you'll need to setup an application password.
Then run cron from the command line and make sure it works. From a terminal, navigate to the installation folder and run the cron.php script:
cd /path/to/osticket
cd api
php cron.php
That should trigger a fetch, if that works, but it doesn't automatically work, then something is wrong with your cron config.
Actually, it's been a while since I used plesk, but make sure you're passing the full path to the script, that helps.
Don't know what your php cli binary is, but this cron command might work:
/usr/bin/php /path/to/osticket/api/cron.php
Because the script isn't executable by itself, you need to call php with it as an argument.
Guide to getting it cron on plesk: https://www.conetix.com.au/support/article/how-set-scheduled-task-cron-job-plesk-12
Depends on your version of plesk, and your level of access etc. They like to restrict access to cron as it can be dangerous to the server as a whole, so it matters what subdirectory your osticket is installed in. I used a wrapper script on my media temple servers when I was working with them and had to use plesk.
:-)
Let me know how you're going.