Hello Anuja, the old LL.B course you are talking about is the 3 year LL.B Programme, if I am not wrong. There are a few universities that still provide this 3 year LL.B course.
There is Maharashtra State common entrance test (MH-CET 2019) for the same. But the last date to apply for this entrance examination has closed on 25 March 2019.
The top participating colleges in this exam are:
1. University of Mumbai, Mumbai
2. Indian Law society college, Pune
3. Government law College, Mumbai
4. Dr. DY Patil Vidya Pratishthan Societys Dr. DY Patil law College, Pune
5. Yashwantrao Chavan Law College, Pune
6. Sinhgad Law College, Pune
7. Rizvi Law College, Mumbai
8. Manikchand Pahade Law College, Aurangabad
9. SVKMs Pravin Gandhi College of Law, Mumbai
10. DES Shri Navalmal Firodia Law College, Pune

And many more, check the link:
https://law.careers360.com/colleges/list-of-law-colleges-in-India?f%5B0%5D=sm_college_course_level%3AUG&f%5B1%5D=sm_college_degree%3ALL.B.&f%5B2%5D=sm_college_state%3AMaharashtra&f%5B3%5D=sm_quali_exam%3AMH%20CET%20Law

Now if you want to apply for any other university for 3 year LL.B, following are the options:
1. University of Delhi (DU) LLB Entrance Test
Application form (Online): 15 April 2019 - 7 May 2019
Participating college: Faculty of Law- Law Centre I&II and
Campus Law Centre

2. BHU - UET (Law)
Application form (online): February 10, 2019 - March 16, 2019
Participating college: Law School, Faculty of Law Benaras
Hindu University

3. LSAT - India
Application form (online) : October 15, 2018 - May 20, 2019
Participating college: Jindal Global Law School OP Jindal Global University, Sonipat

4. Panjab University
Application form (online): 10 April 2019 - 18 April 2019
Participating college: Department of Law, PU Chandigarh

To know about more universities like above, visit the link:
https://www.google.com/amp/s/law.careers360.com/articles/9564-law-entrance-tests/amp

All the best!
I hope this helps.