Hi Prateek.

The admission to all India BAMS courses is done through AYUSH counseling.Ministry of AYUSH has released the schedules of AYUSH BHMS, BAMS, BUMS & BSMS Counselling and Admission Schedule. According to the notification released by Ministry of Ayush, the Online Under Graduate Ayurveda/Siddha/Unani/Homoeopathy Seats Allotment Process cum Counseling will start from 25 June. The registration for the first round of Seat Allotment and Counselling of Under Graduate Ayurveda/Siddha/Unani/Homoeopathy will commence from 25 June 2019 and result of 1 st round of allotment will be declared on 04th July 2019. According to notice, All the NEET Under Graduate (BAMS/BSMS/BUMS/BHMS) aspirant candidates are hereby informed that Counseling for All India Quota seats including Government, Government Aided, Private/ Deemed Universities/Central Universities/National Institutes for the Undergraduate session 2019-20 will be conducted by AYUSH Admissions Central Counseling Committee(AACCC), Ministry of AYUSH, Government of India.

For more details please check :

https://www.ccimindia.org/

It is difficult to find out the exact cutoff score for BAMS since this has been added to neet only recently. However a score of 370 for your category will be safe enough.

Good luck!