Pavol
The current osTicket codebase does not have a responsive UI/UX natively. You would have to modify the codebase to accomplish that. When modifying the codebase you are always on your own as you are deviating from core. You will proceed at your own risk. Good luck!
With this being said a fully modern and responsive UI/UX will be included with v2.0 coming in the near future; so stay tuned!
Cheers.