CLAT is the National level Entrance Exam for five years Integrated Law Programme (B.A LLB) & Post graduate Law (LLM) programme. There is no any Common Entrance Exam for three years Law programme, There are many universities offer this programme but some of the top universities for theprogramme you can prefer Faculty of Law Delhi University, Faculty of Law Banaras Hindu University etc. As per the eligibility to apply you should be Graduate. You can check the eligibility to apply into the colleges with the given below links.

https://law.careers360.com/articles/du-llb-eligibility-criteria

https://law.careers360.com/articles/bhu-llb-eligibility-criteria

Good Luck!