Hii Senthoor!
Sorry, but there are no Colleges in Tamil Nadu providing Horology course. Infact, There are almost no Colleges across India providing this course. If you want to Study time and watch making, you can join Some foreign Institutes offering the course such as-
* North American Institute of Swiss watch making, Fort worth, Texas
* N. G Hayek watchmaking school, Miami, Florida
Etc.,
Hope this helps.
Good luck!