Hello There ,

Yes , private medical medical colleges do have reserved seats under government which are known as semi government seats .The cutoff for them is generally little less than that for fully government colleges , although the fees for semi- government seats is generally high , although a little less than private college fees  , but the fees is decided by the government itself for those seat.

If a student misses a seat in government colleges , they may apply for semi-government seat .

Hope it Helps and All the best .