In the mirror universe, Ranjit Singh was a Terran and a verified descendant of Khan Noonien Singh. In 2288, he was put forth by Ivan West as a candidate to replace Spock as Terran Emperor. This idea was quickly shot down, as most considered Singh to be a megalomaniac. (TOS - Mirror Universe novel: The Sorrows of Empire)

Considering that Khan Noonien Singh's counterpart did not have any children before departing Earth in the SS Botany Bay in 1996, it is highly likely that Ranjit Singh has no analogue in the primary universe.