Hii

There are no other entrance exams for medical field in India.
To pursue MBBS or for that matter any medical course i.e BDS, BUMS, BHMS, BAMS, you need to appear in NEET entrance exam. 
Only AIIMS and JIPMER are two institutes which conduct a seperate entrance exam rest all the colleges and universities accept NEET scores itself for the purpose of admission to MBBS, BDS or ayush courses. The councelling for MBBS and BDS is conducted by MCI.
Incase you wish to study veterinary science, then  also you are supposed to appear in NEET exam itself and the councelling only will be seperate which will be conducted by VCI.
So, there is no other exam you need to appear for, other the the three mentioned, if you are a medical aspirant.

Hope this helps
Thanks!!