Hi Sundeep, You can do MSc in Food and nutrition. It takes 2 years.  Eligibility Criteria (Qualifying Exam) is

Pass with 60% aggregate marks in Bachelors of Science Degree (Home Science or Medical or Non-Medical or Biosciences or Medical Science & Allied Medical or Nutrition & Dietetics or Food Technology) or Veterinary Microbiology & Parasitology or Genetic Engineering & Biotechnology or Clinical Chemistry or Public Health & Allied Sciences or equivalent, subject to qualifying entrance exam (if any).
Top colleges/universities offering this course in India are:
The Women Christian College
School of Health Science, Kerala
Lovely Professional University, Punjab
D Y Patil University, Navi Mumbai
University of Mysore
University of Madras
Central Food Technology Research Institute
Acharya N.G Ranga Agricultural University
Jadavpur University

Dear Sundeep,

Yes, most definitely you can pursue a certificate course in nutrition and dietetics after completing BAMS. Certificate courses are usually of six-months duration. Some colleges and universities which offer a certificate course in nutrition are, Ratnam College of Arts and Science, Maharashtra; Bangalore University; University of Madras, VLCC Institute, and many more.

Good Luck for the future!