In the mirror universe, Ranjit Singh was a Terran male who lived during the 23rd century. He was a verified descendant of Khan Noonien Singh.

In 2288, he was put forth by Colonel Ivan West as a candidate to replace Spock as Terran Emperor. This idea was quickly shot down, as West's co-conspirators 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 counterpart in the primary universe.
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