With the help of homestate quota and choosing non core branch you have possibility to get government college

There are many government university which select candidate on basis of jee main marks for e.g. GURU NANAK DEV University, Amritsar tak candidate on basis of jee main. Marks.

Search near your locality which government university take admission on this basis.

In this type of university you easily able to get seats in core branch 

If you go through jossa than chance of getting core branch is less