If you go into labour there, they’ll take you to a maternity ward in Italy.
And even if you managed to hide away and give birth their, the Vatican doesn’t give birthright citizenship. You’re a citizen of the Vatican if the Pope says you’re a citizen of the Vatican.
The answer is “none”! As Vatican City is the only country to have a zero ‘birth rate’.
If you go into labour there, they’ll take you to a maternity ward in Italy.
And even if you managed to hide away and give birth their, the Vatican doesn’t give birthright citizenship. You’re a citizen of the Vatican if the Pope says you’re a citizen of the Vatican.