Private Colleges do not participate in All India Counselling and they participate only in State Counselling. And for appearing for State Counselling you need to hold the domicile of that particular State. Or else the only other option is through Management Quota. And there are 3 Categories in Private 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 provided the Candidate has registered for the respective State Counselling and has not been able to secure a seat in the Counselling. So if you belong to UP and want to study in Patanjali BAMS College, you can appear for UK State Counselling for Management Quota seats. But you have to participate as Other Category Candidate and not as a Candidate who belongs to EWS. Because out of your State, you cannot claim reservations.  The last Category is NRI seats Category and you cannot apply for that. With a score of 523, you do have fair chances for a seat in this College.