Here I am giving you information about differences between Part Time and Fulltime PhD programe offered by colleges situated in India below :

For admission in full time Phd you have to pass an entrance examination or NET exam with good marks . but for part time PHD you not need to pass any entrance examination you just pass interview process.
The minimum period for full time PHD research work is three years and part time PHD programe duration is four year from the date of registration in the case of Master's degree holders;

The maximum period for completion of the regular Ph.D. programme for Master's Degree holders shall be five years in the case of full-time candidates and six years in the case of Part time candidates.

The maximum period for part time Ph.D. programme for Master's Degree holders shall be five years in the case of full-time candidates and six years in the case of Part time candidates.

Top PHD colleges in India are :
Dhanabagiyam Krishnaswamy Mudaliar College For Women VELLORE
Dharmapuram Adinam Arts College MAYILADUTHURAI
Dharmsinh Desai University NADIAD
Dr B R Ambedkar Open University HYDERABAD
Dr M G R Educational And Research Institute CHENNAI
A.V.C. College MAYILADUTHURAI
A.V.V.M. Sri Pushpam College POONDI
St. Xavier's College,Maharashtra
Indian Institute of Technology, Maharashtra
Indian Institute of Technology, Delhi
Jawaharlal Nehru University,Delhi
Birla Institute of Technology & Science, Pilani,Rajas than
Indian institute of science (IISC),Bangalore.
postgraduate instituteof medical education and research,Bangalore
Amity institute of microbial technology,Delhi
Pearl school of business,Delhi
Indian Institute of Technology,Uttar Pradesh
Acharya N.G. Ranga Agricultural University,Andhra Pradesh
Amrita Institute of Medical Sciences & Research Centre,Kerala
Indian Institute of Technology,West Bengal
you can try also Delhi university for Ph.d programmes in many disciplines.
A.R.C. Viswanathan College MAYILADUTHURAI, Chikkaiah Naicker College ERODE
B.J. Medical College PUNE
Baba Saheb Dr B R Ambedkar College Of Agricultural
Bharath University Chennai CHENNAI
Bharathidasan University TRICHY
Bharathis Womens College CHENNAI .
Choudhury Charan Singh Haryana Agricultural University HISSAR
College of Law VISAKHAPATNAM
Dayalbagh Educational Institute AGRA