yes you can
It is usually advised to fill the JOSAA choices as per the preference of colleges and departments, for example CSE in NIT Trichy is your priority followed by CSE in NIT Warangal, you can fill CSE at NIT Trichy at serial number 1 and CSE at NIT Warangal at serial number 2 and so on and so forth.

but the previous cut off of colleges should be taken in consideration, it is better to research over the cut off of colleges then make a preference list of colleges and fill accordingly

for the college preferences and to know which colleges participate in the JOSAA counselling, please go to the below mentioned link: https://engineering.careers360.com/articles/josaa-participating-institutes/amp

Hello!Mayukh

You are elligible for JEE ADVANCE.With this rank chance of getting government engineering college is very less.You should focus on JEE ADVANCE.Or look for other engineering entrance examination.

Ask for any query.

GOOD LUCK!