Hi, 

Yes for admission into any private college(government quota) domicile certificate is essential

If you hold the domicile of the state in whuch the private college is present then you are eligibke for government quota seats in private college.

However if you do not belong to that state concerned then you wont be eligible for  government quota. Only way through which you can get a seat is via management quota. Hereby you would have to contact the college concerned directly.

Hope it helps
All the best