Aman, there are Private Medical Colleges, Govt. Medical Colleges and Deemed/Central Universities across India that teach MBBS. And admission to these Colleges is thriugh All India and State Counsellings. Private Medical Colleges do not participate in All India Counselling and the seats are filled through State Counselling alone. And for appearing for State Counselling you need to hold the domicile of that particular State. Under All India Quota, All the 15% of All India Quota Seats except for Jammu and Kashmir, Ladakh, 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. Here the fees is usually nothing less than 40 lakhs. The last Category is NRI seats Category and you cannot apply for that.
Now this the counselling procedure. You havent mentioned your Category. With 600, you cannot get any MBBS seat across India if you belong to General Category. Because cut offs for few Colleges are higher. If you belong to any of the reserved Categories, you do have good chance. But in both cases, 600 cannot get you AIIMS or JIPMER.