What ethnicity are Indians?

I assume you're referring to Indians from South Asia, not Amerindians. India is a very multi-ethnic state. Some of the largest ethnic groups are:

-Gujuratis (Gujurat, Daman and Diu)

-Punjabis (Punjab, Haryana, Himachal Pradesh, Delhi, Chandigarh)*

-Bengalis (West Bengal)**

-Paharis (Uttarkhand, Sikkim, Kashmir)***

-Tamils (Tamil Nadu)

-Malayalis (Kerala)

-Kannadas (Karnataka)

-Telugus (Andhra pradesh)

-Tuluvas (a part of Karnataka called Tulu Nadu)

-Marathis (Maharashtra, minority in Goa)

-Konkanis (Goa, minority in Maharashtra. Majority in parts of southern Konkan in Maharashtra as well)

-Kashmiris (Kashmir)

-Ladakhis (Ladakh, a part of Kashmir)

That's just the tip of the iceberg.

Indian ethnic groups are mostly categorized in two large groups, Indo-Aryan or Dravidian. Bengalis, Punjabis, Gujuratis, etc. are Aryans while the Tamils, Malayalis, Telugus, etc. in the south are Dravidians. There are also some Indians of British descent, called Anglo-Indians.

There is a small number of Jews, from a number of different Jewish communities: Cochin Jews (Malayali Jews), Bene Israel (Marathi Jews), Baghdadi Jews (Arab Jews in Maharashtra), Bnei Menashe (Mizo and Kuki Jews, two Christian tribal groups) and Bene Ephraim (Telugu Jews). Many Indian Jews have migrated to Israel.

*Also in Punjab, Islamabad and Azad Kashmir in Pakistan

**Also in Bangladesh

***Also in Nepal and Bhutan

Also in Tamil Eelam in Sri Lanka