India has a rich Jewish history, with the main Jewish communities formerly residing primarily in Mumbai (Bombay), Calcutta and Cochin. During the 1950s and 1960s, these communities nearly entirely immigrated to Israel.
Shavei Israel works extensively with the Bnei Menashe who reside in the northeast of India. More information is here.
Another group in India is the Bnei Ephraim, a small community in rural India that claims to be the descendants of the biblical tribe of Ephraim, exiled from the land of Israel nearly 3,000 years ago. We have have more information here.
While not specifically identifying themselves as Jewish, a group of 650 Pathans in the village of Malihabad, 25 kilometers from the Indian city of Lucknow, also claim to be descendants of the lost tribe of Ephraim. They have some customs that resemble Jewish tradition. We have more information on this group here.