hi!
yes, you can do PhD in genetics or any other course after your MD Infact, many of the renowned scientists of India like Dr. Vineeta Bal and Dr. Satyajeet Rath switched into research after their medicals. Indeed, it gives you an edge as you are well versed with human physiology and do not only know the molecular or cellular aspects of it. This helps in approaching a problem in a more viable, practical and patient directed way. It's still not that bad situation in india for PhD as like normal engineering degree.
So, It would be definitely helpful to you.
Do consider the commitment required for doing PhD as it would take minimum 4 years. Its even more than that in case you are doing it part time.
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