It should be an easy question to answer but it isn’t.
This is because osTicket Awesome uses different favicons depending on which color theme you have currently selected.
The quickest solution is to have two versions of your favicon (named favicon.ico and favicon.png) and to drop them into the directory that corresponds with the theme you are using.
If you want to use the nuclear option you can drop them into all of the theme directories. You will find the directories here:
/osta/css/themes