Dear Sahaana, for BSc Anasthesia course in Tamil Nadu you can go for the following colleges -
* 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

I hope this helps you!

Hii!
Some of the Colleges offering the BSc anesthesia ourse in tamilnadu are-
* Annamalai University
* Shri Ramchandra University
* SRM University
* Christian Medical College
* Surabhi school of Nursing
* Vinayak mission university
* Hindustan Institute of Technology and Science
Etc.,
Hope this helps.
Good luck!