In Gujarat, we have Government Medical Colleges and Private Medical Colleges. Under All India Quota, All the 15% of All India Quota Seats except for Jammu and Kashmir, 100% Seats at Deemed and Central Universities, IP Quota seats in ESIC Colleges, Seats at AFMC, AIIMS and JIPMER are filled by DGHS. The 85% State Quota and Private Colleges are filled by the respective State Authorities. And there are 3 Categories in Private Medical Colleges. Category A is the Government Quota Seats. And only candidates of the home State are eligible to apply for these seats. B Category seats are also called Management Quota Seats and they are filled through State Counselling and the remaining seats are filled through direct Admissions by contacting the College directly provided the Candidate has registered for the respective State Counselling and has not been able to secure a seat in the Counselling. Here the fees is usually nothing less than 40 lakhs. The last Category is NRI seats Category and you cannot apply for that. So to answer your question, Government Medical Colleges only participate in All India Counselling for their 15% seats. And the Government Medical Colleges of Gujarat are:

BJ Medical College

Surat Medical College

Baroda Medical College

MP Shaw Medical College

Sola GMERS Medical College

Bhavnagar Medical College

Pandit Deendayal Upadhyay Medical College

Vadodara Medical College

Gandhinagar GMERS Medical College

Nanakwada Medical College

Maharaja Sayajirao Medical College