As you have asked about the scholarship for Indian students to study abroad for PhD course, I am mentioning some of them, check below for the details

Some of the states and central government offers scholarships to the students. Here's a list of scholarship for Indian students:

Dr Manmohan Singh Scholarships
Oxford and Cambridge Society of India Scholarship
USIEF Fulbright-Nehru Fellowships
Chinese Government Scholarship
International PG Research Scholarship by Australia
Huawei Maitree Scholarship for study in China
Raman-Charpak Fellowship for Indian and French Ph.D students
Tata Scholarship for Cornell University,
US UCD UG scholarship
Oxford University's Rhodes Scholarship
University of Sheffield's Scholarship
India4EU II Scholarship to study in Europe
Commonwealth Scholarship and Fellowship
Inlaks Scholarship
Hornby Scholarship to study in the UK
Melbourne - India PG Scholarship
University of Sessex Scholarship