A couple existing RPG products with Indian subcontinent type material:
Gods, Demi-Gods, Heroes, 0e. A D&D interpretation of the Hindu pantheon.
Arrows of Indra an OSR OD&D based fantasy mythic India setting and RPG.
Nightstorm is a Basic D&D module set in the Mughal India inspired realm in the Hollow World Campaign setting. The outer world of the Mystara basic campaign setting has a fantasy India land called Sind, but that is mostly developed in Dragon articles and small references.
Legends & Lore 1e. A D&D interpretation of the Hindu pantheon.
Legends & Lore 2e. A D&D interpretation of the Hindu pantheon with some discussion about the cosmology and such as well.
Ravenloft 2e and later editions. The horror setting includes a fantasy Indian themed island domain.
Web of Illusion 2e adventure module set in the Indian themed Ravenloft domain.
Mahasarpa. 3e Web Enhancement PDF fantasy India setting adaptation of Oriental Adventures.
Mindshadows. 3e setting book by Green Ronin focusing on psionics and a loosely Indian themed high psionics setting.
Imperial Age British India is a d20 Modern supplement from Adamant Entertainment.
Dog Soul Publishing came out with their 3.5 fantasy India setting Sahasra, some support supplements and adventures, and 3.5 books of faith sourcebooks on Hinduism, Jainism, and Sikhism.
Pathfinder's Golarion setting has a fantasy India type continent called Vudra and at least one module set there.
Mythic Monsters 41: India is a short India themed Pathfinder 1e bestiary from Legendary Games.
Dhanurvidya & Varman: The Arms & Armor of India is a 4e supplement from Skirmisher Publishing.
Beasts from the East India is a 5e Indian themed bestiary.
For non-D&D there is
Against the Dark Yogi Mythic India Roleplaying.
Ironsworn India/Hindu Mythology Flavor Pack
Asian Bestiary I for Hero games includes India among other Asian countries covered.
Asian Bestiary II for Hero includes Tibet among other Asian countries covered.
Tales of the Caliphate Nights is a True20 setting of the Golden Age of Islam which spreads across from the Middle East into India and beyond.
The Children of Fear is a massive Call of Cthulhu adventure exploring myths and legends of central Asia and India.
Tibet the Roleplaying Game.
Secrets of Tibet is a Call of Cthulhu supplement. There was an older edition Mysteries of Tibet as well.
Mysteries of the Raj was a Call of Cthulhu supplement.
There are others out there.