Hello Arnab,
Extension and development Studies is a multidisciplinary branch of social science which addresses issues of concern to developing countries.
It is good to listen from you that you want to pursue PG in this subject. This is a unique and very interesting subject to study.
Here sharing a link from which you can get the idea of your query a bit.
http://dqxeclau.top/university/jamia-millia-islamia-new-delhi/ma-development-extension-course
There are certain colleges all over india those offer MA in extension and development.

• IGNOU
• Jamia Millia Islamia University
• Christ University
• National institute of agricultural extension management, Hyderabad
• IIT Guwahati
• IIT Rourkela
• Azim premji university, Bangalore
• Ambedkar college, Tripura

Career Option:

• Policy Maker
• Researcher
• Administrator
• Social Worker
• Social Studies Teacher
• Community Service Officer
• Policy Analyst
• Business Studies Teacher
• Agency Development Manager
• Teacher & Lecturer etc.

Hope the above information helps
All the best!