The government quota seats in private colleges are only designated to the state domicile students. Now if you are domicile of Gujarat then you have to apply in Rajasthan on the basis of All India Quota. So suddenly you will not be able to go for Government Quota seat in Rajasthan Private Medical college.

To know more about the Private colleges in Rajasthan visit the link below:

https://medicine.careers360.com/colleges/list-of-private-medical-colleges-in-rajasthan

To know more about NEET visit the link below:

https://medicine.careers360.com/exams/neet

I hope this answer helps. All the very best for your future endeavors!