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