Dear Anmol, there are a few entrance examinations apart from JEE so I'll be mentioning a few of the top engineering entrance exams.

• BITSAT is also known as the BITS Admission Test organized by the Birla Institute of Technology and Science (BITS) Pilani.If you wanna apply for the BITSAT 2020 examination then application form will be available from the third week of December 2019 (Tentatively).
• VITEEE is conducted by VIT (Vellore Institute of Technology) and offers admission in VIT Vellore, VIT Chennai, VIT-AP, VIT Bhopal institute. If you wanna apply for the VITEEE 2020 examination then application form has been going on and the last date to submit the form is 29 February 2020.
• SRMJEEE is conducted by the SRM Institute of Science & Technology (SRMIST) for offering admissions in Engineering courses and conducted once in a year.If you wanna apply for the SRMJEEE 2020 examination then the application form will be available soon
• KIITEE will be conducted by Kalinga Institute of Technology, Bhubaneswar (KIIT) and conducted once in a year. If you wanna apply for the KIITEE 2020  examination then the application form will be available from the Third week of November 2019 (Tentatively).
• IPU-CET: Guru Gobind Singh Indraprastha University will conduct IPU CET 2019 to invite admissions into the following programmes: B.Tech, BBA, BCA, BJMC, LLB, BHMCT, M.Tech, LLM, MBA and MCA
• Karnataka Common Entrance Test (KCET)  will be conducted by Karnataka Examinations Authority (KEA) for admission of candidates to various Engineering, B. Pharm and Farm Science courses in Government/University/Private Aided/Private un-aided institutions in Karnataka State.
• West Bengal Joint Entrance Examination (WBJEE) is a state-level exam conducted by the West Bengal Joint Entrance Examinations Board (WBJEEB).  WBJEE 2020 will be conducted by West Bengal Joint Entrance Examinations Board in offline mode on February 2, 2020.

These were some of the most popular engineering entrance exams preferred by students.

All the best

Hope this helps