I am a research scholar in IIT Hyderabad. I need to go to Turin, Italy from 1st September to 31 st October a total of 61 days and from there I need to travel to Amsterdam, the Netherlands from 1st November to 20th December a total of 50 days, so a total of 111 days in Europe for my research work. What is the Visa type?
Your planned stay in the Schengen area exceeds 90 days in a 180-day period. Therefore, you need a type D visa for at least one part of your stay. The other part of your stay could be a type D visa or a type C visa.
The problem you will face is that you're not staying in either country for more than 90 days, so each country could refuse to issue the type D visa on the grounds that your stay in that country is too short. Your best bet is probably to apply for a type C visa from Italy for the first part of your stay, and then, after it is granted, apply to the Netherlands for a type D visa for the second period. In the second application, you will have to point out that you cannot use a type C visa for that period because you will have been in Italy in September and October.
It is possible (likely, perhaps), that the Netherlands will grant a type-C "visa with limited territorial validity" under Article 25(1)(b) of the Schengen Visa Code:
1. A visa with limited territorial validity shall be issued exceptionally [...]
(b) when for reasons deemed justified by the consulate, a new visa is issued for a stay during the same 180-day period to an applicant who, over this 180-day period, has already used a uniform visa or a visa with limited territorial validity allowing for a stay of 90 days.
If you have host institutions in Italy or the Netherlands, you should ask whether they have an office that supports foreign researchers, and, if they do, seek advice from those offices.