Depending on the legislation of a particular country to which the parents of this child belong.
If we talk about Russia, I would say that citizenship will be acquired by birth. So, in accordance with paragraph 1 of Article 12 of the Federal Law of May 31, 2002 No. 62-FZ "On Citizenship of the Russian Federation", a child acquires citizenship of the Russian Federation by birth, if on the child's birthday:
a) both of him the parent or his only parent has the citizenship of the Russian Federation (regardless of the place of birth of the child);
b) one of his parents has the citizenship of the Russian Federation, and the other parent is a stateless person, or recognized as missing, or a place his location is unknown (regardless of the child's place of birth);
c) one of his parents has citizenship of the Russian Federation, and the other parent is a foreign citizen, provided that the child was born on the territory of the Russian Federation or if otherwise if he becomes a stateless person;
d) both of his parents or his only parent living in the territory of the Russian Federation are foreign citizens or stateless persons, provided that the child was born on the territory of the Russian Federation, and the state of which his parents or his only parent are citizens does not grant the child its citizenship.
Now, regarding the last two subparagraphs. What is considered the territory of the Russian Federation?
Outer space and space bodies in themselves are a territory under international jurisdiction, the sovereignty of any state does not extend there, and they are in the common use of mankind. Accordingly, if it happens that a child was born in outer space, or on an asteroid, or on another planet, if it is not clear how his parents got there, then it turns out that he was not born on the territory of the Russian Federation and then subparagraphs "c" and "g" do not work.
If the child was born on a spacecraft, then here we need to already turn to international space law.
So, in accordance with Article 2 of the Convention on Registration of Objects Launched into outer space, these objects by the launching state (that is, the state that carries out or organizes the launch of a space object, or the state from whose territory or installations the launch of a space object is carried out) must register in a special national register. When there are two or more launching States for any such space object, they jointly determine which of them will register the object.
The Outer Space Treaty notes that the State Party in whose register the space object is entered, launched into outer space, retains jurisdiction and control over such an object while it is in outer space, including on a celestial body.
Thus, if a child was born in spaceany ship, even if it is standing on some planet, and registered by Russia in the register, it will turn out that it was born on the territory of Russia and then the subparagraphs "c" and "g" will work.
As a rule, the ship is the territory of the state to which it belongs. Therefore, citizenship is determined by the ownership of the ship. In space, a child can only be born on a ship, someone's country. If the child is born outside the ship (and what if?), Then the child will not light up the Earthman's passport :)
Probably like the parents. The situation is almost the same if the child was born on a ship in the ocean. Well, or at worst it will be stateless.
b) by the right of blood
c) the state to which this expedition belongs.
Correct if anything.
P. S .: I'm from the future. If he is born in open space, then I feel sorry for him and his mother.