Hello student yes some Private university in India offer part time PhD in law you can pursue it by applying for the same.
Lovely professional university and Amity University are on top private institute to  offer part time PhD in law. But I'll suggest you if you're really intrested in doing PhD in law then prefer regular instead of part time because there's no comparison between part time PhD and regular specially in law.

Feel free to comment if you have any doubt
Good luck

Hello Sreejith, there is a part time course of PHD in law, some of the best colleges are

Rank	Universities / Colleges	Location
1	National Law School of  India University	Bangalore
2	National Academy of Legal Studies and Research	Hyderabad
3	West Bengal National University of Juridical Sciences	Kolkata
4	National Law University, Jodhpur	Jodhpur
5	National Law Institute University	Bhopal
6	SRM university	Haryana
7	National University of Advanced Legal Studies	Kochi
8	Dr. Ram Manohar Lohiya National Law University	Lucknow
9	National Law University, Odisha	Odisha
10	National University of Study and Research	Ranchi
11	Hidayatullah National Law University	Raipur
12	Rajiv Gandhi National University Of Law	Patiala
13	National Law University and Judicial Academy	Guwahati
14	Chanakya National Law University	Patna
15	National Law University, Delhi	Delhi
16	Faculty of Law, Aligarh Muslim University	Aligarh
17	Faculty of Law, Jamia Millia Islamia	Delhi
18	Indian Law Society’s Law College	Pune
19	Government Law College	Mumbai

Hope this helps.

Thank you.

Yes, Savetha school of Law, Saveetha University, Chennai offers a part time PhD in law. The duration of the course is 4 years. As per the eligibility criteria, Candidates should have passed LL.M degree and as per the norms prescribed by the recognized university. Medium package offered is around 5.7 lakhs per annum.
You can download the brochure from the given link-
http://www.careers360.com/colleges/saveetha-school-of-law-saveetha-university-chennai/courses?degree=14

Saveetha School of Law, Saveetha University, Chennai

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