Hello Abhishek,
There are many Universities all over India who conduct their etrance exam for persuing astronomy. The basic criterion required for admission in any course of astronomy is passing the class 12. Students can do graduation and also can get specialization in astronomy. Below there is a list of all the entrance exams conducted for astronomy in India

• Aligarh Muslim University Entrance Exam
• Andhra University Entrance Exam
• Aryabhatta Research Institute of Observational Sciences (A.R.I.E.S.), Joint Entrance Screening Test
• Bangalore University Entrance Exam
• Birla Institute of Technology - BITSAT Entrance Exam
• Cochin University of Science and Technology Entrance Exam
• Cochin University of Science and Technology: Department of Atmospheric Sciences Entrance Exam
• Dr Babasaheb Ambedkar Marathwada University Entrance Exam
• Harish Chandra Research Institute, Allahabad (Uttar Pradesh) Combined Research Entrance Exam
• Indian Institute of Astrophysics Entrance Exam
• Indian Institute of Geomagnetism Entrance Exam
• Indian Institute of Science (IISc.): Department of Physics, Bangalore (Karnataka) Entrance Exam
• Indian Institute of Technology - Joint Entrance exam
• Inter University Centre for Astronomy and Astrophysics (I.U.C.A.A.), Pune (Maharashtra)
• IUCAA NCRA admission test (INAT) (set by the National Centre for Radio Astrophysics, Tata Institute of Fundamental Research (NCRA-TIFR), Pune)
• JNTU College of Engineering Entrance Exam
• Madurai Kamaraj University Entrance Exam
• Mahatma Gandhi University Entrance Exam
• Osmania University Entrance Exam
• Patiala University Entrance Exam
• Physical Research Laboratory (PRL) All India Common Medical Entrance Test
• Punjab University Entrance Exam
• Punjabi University Entrance Exam
• Raman Research Institute Entrance Exam
• Raman Research Institute Joint Entrance Screening Test
• S N Bose National Centre for Basic Sciences Joint Entrance Screening Test
• Shivaji University Entrance Exam
• Swami Ramanand Teerth Marathwada University Entrance Exam
• Tata Institute of Fundamental Research Common Admission Test
• Tezpur University Entrance Exam
• The Indira Gandhi National Open University Entrance Exam
• University of Chennai Entrance Exam
• University of Kolkata Entrance Exam
• University of Lucknow Entrance Exam

You can choose any of the above according to you choice and comfort.

Good luck.