Government Medical College

No, with a rank of 6 lakh, you can not get admission into the Government Medical College (GMC), Kota, even within your home state or category-based quota. The GMC, Kota, is a top medical college where the cutoff rank usually remains under 10,000, and it was 9971 in 2021 for MBBS.
However, you may get MBBS at a few other selected medical institutes like Sukh Sagar Medical College and Hospital (M.P. ), where the closing rank was around 606752 in 2021.
Otherwise, you can use the Shiksha platform's NEET College Predictor 2022 (https://www.shiksha.com/medicine-and-health-sciences/neet-college-predictor) to get more specific recommendations based on the courses and states you may get with this rank. Here you need to enter your NEET rank, gender, category, and domicile to get idea of possible colleges.

Five states - Gujarat, Rajasthan, Punjab, Haryana and Himachal Pradesh - and Puducherry have government medical colleges with NRI quotas. Unlike caste-based quotas, which are to compensate for historical deprivation and backwardness, the NRI quota is for being able to charge Lakhs as fees. Most states claim the quota is to mobilise funds for maintenance and infrastructure, something that would earlier have come from the health budget. Gujarat has the highest number of NRI seats 241, followed by Rajasthan with 212, Punjab with 41, Puducherry with 22, Himachal Pradesh with 20 and Haryana with 15 seats. NRI seats are open not only to NRIs but also those they sponsor. Thus, many can use this quota if they have a brother, sister or parent who is an NRI willing to give an undertaking to sponsor the entire course fee. If a student has no parents or is taken as a ward by near relatives, even NRI uncles, aunts or grandparents can be sponsors.