I m from general category and scored 53 in jee mains and got 82% in board exams can i get any govt. College for btech ?

I need govt. College because i cannot pay higher fee amount of engineering colleges. What should i do now? Should i fill forms for the colleges i know or wait for the jee counselling. Actually i don't know what to do when the rank will be declared on 7th of july and what to do before.