Yes, of course, you can. Even My father is an EX-serviceman and I am also an Army brat unlike you.
You will undergo through all the stages of getting the scholarship as a normal student. Also, I will suggest you to apply for PMSS (Prime minister scholarship scheme ) provided to the wards of Ex-serviceman. Visit your nearest Zila Sainik board after taking admission to the allotted college. PMSS scholarship grants you a scholarship amount of 30,000 per year.
(NOTE: Don't mention in PMSS application that you have applied for PMSSS also. )
Read a related answer by clicking on the link below.
Is "pmss " and "pmsss" scholarship same if not , what is the difference ? - pmsss.in