Hello Manish,
First of all their are no paid Seats in any Government medical colleges in any state across India.
To get a seat in Government medical college you have to score really good.
Second, if you want to take admission in a government medical college in Rajasthan and you belong to Delhi then you can definitely apply for Rajasthan colleges but for government colleges you will be considered in All India qouta and cutoff for that goes really high.
I hope this helps.
All the best for the future!!

Dear Manish, Rajasthan is not an Open State. The 85% State Quota and Private Colleges are filled by the respective State Authorities. There is no paid seat concept in Government Medical Colleges. It is available in Private Medical Colleges alone.  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 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.