According to some legends, Jews first came to India as King Solomon’s merchants in search of materials for his first temple in Jerusalem. After the collapse of the Second Temple, South Indian Christian tales confirm that Jews settled in Cochin in the first century C.E.
Over the next several centuries, other societies arose, including the Bene Israel, who are supposed to be a Lost Tribe who arrived in western India 1,000 years ago. In the 17th century, Spanish and Portuguese Jews arrived in Madras and Goa. Baghdadi Jews went to western India, then to Mumbai (formerly Bombay) and Calcutta, from Iraq, Iran, Afghanistan, and other Arab nations in the early 18th century. Later converts and arrivals can be found all around the country, especially in Delhi.
While there is still a small Jewish community in India, the majority of the country’s 30,000 Jews either departed in 1947, when India got independence from the United Kingdom, for the English-speaking world, or made aliyah the following year, when the State of Israel was established.
Source: http://www.jewishledger.com/2015/05/exploring-the-jewish-communities-of-india/