Does an Apple Watch cellular bought in the US work in India

An Apple Watch purchased in USA will only work on North American cellular networks. It will not connect on Indian networks and you will be wasting your money if you want to use it mainly in India. Please see Apple Watch - Carriers - Apple for details of the different cellular models and regional compatibility.

You are correct, in that carrier eSIM support is required, but the question was about a US watch working in India, not which Indian carrier would work. A US watch won't work with any Indian carrier, even those that support eSIM, because the RF bands are different. Both eSim support and the correct bands are needed.

@Rudegar please stop misleading users with false information about regional compatibility for LTE watches. The incompatibility is all about cellular frequency bands approved in different regions. All supporting carriers support eSIM but the frequency bands are different around the world. Apple Watch - Carriers - Apple

it will only work with carriers which support eSIM What is an eSIM and how will it change your future devices for the better? - Pocket-lint so ask your carrier

I do no such thing

only carrier in my country which support apple watch are 3

all info and tech articles about the fact why the bigger carriers here do not support apple watch is down to inability to support eSIM I could link you to some articles but I doubt you'd be able to understand the language