India was a country in the south-central Asian continent on Earth. The people and culture specific to India were referred to as Indian.
When Jack told T'Mir about the places he wanted to visit, he also mentioned India, as this country had "these mystics called fakirs. Supposedly, they can almost stop their hearts just by using willpower." (ENT: "Carbon Creek")
In 1962, Vic Fontaine sang the song "Come Fly with Me" at his nightclub. One of numerous exotic locales mentioned in the song was the Indian city of Bombay. (DS9: "His Way")
Lieutenant Marla McGivers identified Khan Noonien Singh as being from northern India, a region populated by Sikhs during the late 20th century. She described them as "the most fantastic warriors." (TOS: "Space Seed")
By the 24th century, the Federation's Star Station India had been named in honor of this nation-state. (TNG: "Unnatural Selection")