Vatican City

Vatican citizenship is held by very few people.

An excerpt from the article 21 facts about Vatican City

Theoretically, one cannot be born in the Vatican, as there is no hospital with a delivery room there. Vatican citizenship is not inherited from parents at birth, nor is it acquired by being born on the territory of this city-state. One becomes a citizen when performing certain functions in the Holy See and is always granted temporarily. It never replaces another citizenship.