Hi

Once you have declared a certain category in JEE mains you can't change it. If you have declared yourself in general category it remains the same throughout till the counselling. To get into government colleges you need a high cutoff for general category or you can get in with a caste certificate in a comparatively low cutoff. Now you will have to check previous year cutoffs for general category for these colleges if you can get in then its good.

To see the options you have according to your rank and category check this link

Hope this helps.

All the best!