There are a number of colleges in Tamil Nadu offering BSc anaesthesia course. Some of them are -
* G. Kappuswamy Naidu memorial hospital , Coimbatore
* Shree Balaji medical College and hospital, Chennai
* Thanjavur medical College, Thanjavur
* Shri Ramachandra medical College and research institute, chennai
Etc., Click on the link provided below to get more information -
https://www.google.com/amp/s/www.careers360.com/question-best-college-for-bsc-anesthesia-in-tamilnadu/amp
Hope this helps.
Good luck!