I’m pretty sure that this is a technical limitation of PHP.
I’ve heard that other programing languages, such as Ajax, allow the user to submit form data without a page refresh.
In order to achieve the behavior you want you would have to modify the osTicket source code.
It is way beyond the support I can offer, but it is an interesting question and I think I found the solution.
You would need to do something like this:
https://stackoverflow.com/questions/11950509/is-it-possible-not-to-jump-to-the-top-of-the-page-on-form-submit
I hope this helps.