Lawyer exams

To become a member of bar council of India, you need to clear National Bar exam or the bar exam for respective state you want to become member of. However, only LLB degree holders are eligible for sitting in bar exams. Unfortunately you cannot do LLB from open university as there is no provision for it. LLB is a full time course and can be done only from an accredited university recognised by University Grants Commission. You can do Diploma courses in law but you would still not be eligible for the bar exam.

You need to apply for CLAT exam or entrance exam for other universities having their own entrance exam and interview for the admission process.
You can check this link for top law colleges and their admission process:
https://www.shiksha.com/law/ranking/top-law-colleges-in-india/56-2-0-0-0
And, for LLM programme when you are in the final year of LLB degree, you can apply and again you have to apply for CLAT or entrance exam for different universities.