You may follow the technique from this article:
(Displaying Help Topic Based on Selected Department in New Ticket Form at Client Side of osTicket v1.6 RC5)
In your case, then the Category selection of yours is equal to the Department selection of that MOD above, whereas the Sub-Category selection of yours is equal to the Help Topic selection of the MOD.
Does it make sense for you?
Sincerely,
Masino Sinaga