You haven't mentioned whether you have been born in Bihar or if your OBC Certificate is just from Bihar. We will need that information for us to help you with whether you can participate in Bihar State Counselling. On the other hand, according to https://medicine.careers360.com/articles/rajasthan-mbbs-admission , if either of your parents have resided in Rajasthan for a period of 10 years or if you have studied in Rajasthan for a period of 5 years, you are eligible to participate in Rajasthan State Counselling. So by the virtue of your parents living in Rajasthan since 20 years, you are eligible for participating in Rajasthan State Counselling. Because you haven't mentioned whether you studied in Rajasthan or not. Irrespective of that factor, you are eligible for participating in Rajasthan State Counselling.