It largely depends on what you mean by ‘famous’, ‘Jewish’ or ‘in Indian history’.
The Jews with the biggest direct influence on Indian history were probably three British colonial administrators: Edwin Montagu (1879–1924), Rufus Isaacs (1860–1935) and Leo Amery (1873–1955). Montagu served as Indian Secretary from 1917-22 and recommended the reforms that led to the Government of India Act 1919, the first British step towards Indian self-rule. Isaacs served as Viceroy from 1921-26, aiming for a more conciliatory approach than his predecessor but using violence on multiple occasions. Amery, whose mother was Jewish (and who himself was born in India), served as the antepenultimate Indian Secretary from 1940-45, but was frequently frustrated in his role by Churchill.
The Indian Jew with the biggest direct influence on Indian history, meanwhile, may well have been J.F.R. Jacob (1921–2016). Born in Kolkata to an Indo-Iraqi Jewish family, Jacob is best known as the chief of staff of the Indian Army's Eastern Command during the Bangladesh Liberation War, which resulted in the creation of Bangladesh. He later served as the governor of both Goa and Punjab.
The Indian Jew with the biggest international influence, though, may be Yusuf Hamied (born 1936), the chairman of the pharmaceutical company Cipla. Born to a Lithuanian Jewish mother and an Indian Muslim father, Hamied has led efforts to eradicate AIDS and other diseases in the developing world by offering low-cost generic drugs, often against the wishes of the large Western pharmaceutical companies.
(Special mention here also goes to Waldemar Haffkine (1860–1930), a Russian-born bacteriologist who developed and tested the first vaccines against cholera and the bubonic plague while based in India, inoculating millions of Indians.)
Of course the question didn't actually ask about influence per se, but rather fame, which is a bit different and even less well defined.
Internationally the best known Indian Jew right now might well be the British sculptor Anish Kapoor (born 1954). Born in Mumbai to an Indo-Iraqi Jewish mother and a Punjabi Hindu father, Kapoor is known for his use of large abstract biomorphic forms, and was the first living artist to be given a solo show at the Royal Academy of Arts.
The best known Indian Jew who was active in India, meanwhile, may have been the Bene Israel poet Nissim Ezekiel (1924–2004), one of the foremost exponents of English-language verse in India. Alternatively it may have been the spiritual guru Mirra Alfassa (1878–1973), aka The Mother, who was the French-born collaborator of Sri Aurobindo and the founder of his ashram.
