Judaism was one of the first foreign religions to arrive in India and assimilate with local traditions through cultural diffusion. The Jewish population in India is hard to estimate since each Jewish community is distinct with different origins; some arrived during the time of the Kingdom of Judah, others are seen by some as descendants of Israel's Lost Ten Tribes. Of the total Jewish population in India, about half live in Mizoram and a quarter live in the city of Mumbai.

Unlike many parts of the world, Jews have historically lived in India without anti-Semitism from Indians, but tthey have been victims of anti-Semitism from the Portuguese and the Christian Goa Inquisition during the colonial rule. The majority of Hindu community have been very tolerant towards most other religions in India including Judaism. Jews have held important positions under Indian princess in the past and even after independence from British Rule, they have risen to very high positions in government, military and industry. Anti-Semitism in India has manifested itself through the rhetoric of Islamist outfit Lashkar-e-Toiba, who have declared Jews and Hindus to be enemies of Islam

there are five native Jewish communities in India its divided to:

The Cochin Jews who arrived in India 2,500 years ago and settled down in Cochin, Kerala as traders.
The Bene Israel arrived in the state of Maharashtra 2,100 years ago.
The Baghdadi Jews arrived in the city Mumbai from Iraq, Iran, and Afghanistan, and Arab countries about 250 years ago.
The Bnei Menashe are Mizo and Kuki tribesmen in Manipur and Mizoram who claim descent from the tribe of Menasseh.
The Bene Ephraim (also called Telugu Jews) are a small group who speak Telugu; their observance of Judaism dates to 1981.

(source wikipedia)