With a NEET PG rank of 37,360 in the OBC category, securing a seat in a government medical college through the All India Quota (AIQ) is possible, but it will depend on the specific department you are interested in and the competition in that particular year. Typically, some of the less competitive specializations such as:

1. Anesthesia
2. Community Medicine
3. Forensic Medicine
4. Pathology

These departments often have lower cutoffs compared to more sought-after specialties like Radiology, Dermatology, and General Medicine.

In recent years, candidates with similar ranks have successfully secured seats in these less competitive departments, particularly in government medical colleges located in less urbanized or remote areas. However, availability also depends on factors such as the number of seats available, the total number of candidates, and the counseling rounds. It's advisable to participate in all rounds of counseling, including the mop-up rounds, as seats may open up due to withdrawals or other reasons.

For the most accurate information, it is recommended to check the official NEET PG counseling results from previous years to get an idea of cutoff trends.