Unfortunately, the answer is that there is no scope of astrobiology in India. I will tell you my experiences in this regard.
I have been an enthusiast for this subject since class 10. The pursuit of this subject led me to Indian Institute of Science, the topmost research institute in India(where I'm an undergraduate now). The people working here have heard of the term but no one has worked on it. Hence, I've had to depend upon online courses from Coursera.org and edX.org to satisfy my curiosity.
Not to be disheartened, I've tried to search for places where such research could be done. One such place is Indian Astrobiology Research Centre (IARC). However it currently does not have any internship program but offers a diploma program in Astrobiology. Also the people in it are generally enthusiasts from a wide scientific background from all over India and thus are not in general professionals in this field.
Research in this area occurs in isolated pockets throughout the world. The general information regarding these places and the type of research in them can be obtained here:
https://astrobiology.nasa.gov/nai/Note that there are no Indian institutes as affiliates or collaborators, but only IARC is mentioned as the lone place in India where knowledge of Astrobiology can be obtained. As there is no institute which focuses on Astrobiological research in India, it is difficult to get recognition as an affiliate or a collaborator. I do not see this becoming possible in the near future.
Astrobiology as a subject is fascinating. But it is not going to grow in its scope until and unless there is some some development which would sound great to the government and to the public. So, when my friends give me a blank stare when I tell them about this subject, it is not their fault. Yes, the name sounds 'fancy' (and 'ridiculous') because we in India have inherently learnt to associate topics to specific subjects and hence fail to appreciate the interdisciplinary nature of Science. Until and unless this mentality changes, nothing more can be done.
So, the only way to get research done is to try and get into some of the institutes provided in the link, which is again quite difficult. So, Indians generally do not have many options today.
I sound quite pessimistic but all I have told is the truth about the current scenario. But I have not lost hope and I believe you shouldn't too.
Unfortunately, the answer is that there is no scope of astrobiology in India. I will tell you my experiences in this regard.