Apple Watch Series 3 (GPS + Cellular) is not currently available to buy in India.
Apple Watch Series 3 (GPS + Cellular) is not locked to any specific carrier and has a built-in eSIM that copies information from the iPhone's SIM card.
The built-in cellular features require a carrier plan for your iPhone in your country of use that specifically includes support for Apple Watch, including the carrier activating the device on the plan.
If buying Apple Watch Series 3 (GPS + Cellular) in another country, then you would need to buy a model that supports the relevant LTE and UMTS bands for your intended country of use and your supported carrier there.
There are three different regional versions of Apple Watch Series 3 (GPS + Cellular), each supporting different LTE and UMTS bands, as detailed here - there are currently no listed carriers for India:
Apple Watch - Carriers - Apple
If in doubt, I suggest that you contact your intended carrier to ask whether any given model can be used on their network with a plan that they may offer or plan on offering for iPhone that supports Apple Watch Series 3 (GPS + Cellular).
The built-in cellular features cannot be used when roaming. Also keep in mind that warranty service availability may be restricted.