Pregnant woman gets on a plane in Vancouver British Columbia Canada. Gives birth over Nebraska. Lands in Maryland.
What state does the birth certificate say the child is born in, and is the time of birth adjusted to that state's time zone?
Skyborn are a known phenomenon.
Generally, the kid automatically gets citizenship from his mom (and father) through bloodline, so our skyborn on that plane is likely that citizenship(s). There are cases that can't grant a citizenship that way (among them: Vatican is only granted ex officio)
The sky is also treated as an extension of the land below. If the country you fly over has Jus Soli, it grants citizenship to the baby born above it. The USA has Jus Soli in its 14th amendment, our skyborn baby has dual citizenship to whatever country the mom is from.
And in case the plane is over unclaimed water - think a nonstop flight Vancouver-Tokyo by Lufthansa - maritime law applies: The airplane is registered somewhere and treated as territory of that land while over international water. Lufthansa is in Germany, so the kid is, on paper, born in Berlin Germany (as that is what Germany prescribes for air- or seaborn). Germany does not use the unrestricted jus soli but the first test is the bloodline to determine what's the kid's citizenship is, unless the kid would have no citizenship through bloodline. So, if any one parent is German, the child is German. jus soli applies mostly to children of someone who has a permanent residence permit for at least 3 years and has been in Germany for the last 8 years: then the kid is (also) German, even if that grants dual citizenship - till the child is 23 and has to choose one of its citizenships. However, if all known parents are stateless or can't grant the kid citizenship through their bloodline (Yes, that happens!), then the kid born on this international flight has the right to become a German citizen - but some rules still apply.
Now, which state's office is responsible? That is even more tricky. Technically, OP's kid that is born in Nebraskan Airspace is a Nebraskan, so it should be a Nebraskan birth-certificate. But the general rule in maritime practice would be to file the papers in the next port the ship lands, that would be Maryland if applied to planes.
For a german registered ship or plane (my Lufthansa example), the responsible municipality would be Berlin, unless another municipality is responsible.
And then, I thank hszmv for this US Addendum:
It should be pointed out that in the U.S. state citizenship is based on primary residency and can be changed over time. I've personally been a Maryland citizen, a Florida Citizen, and a Maryland citizen for a second time in my life. Usually state citizenship denotes exclusively where your vote is cast. No state can restrict a U.S. citizen from taking up residence in that state per constitution. So the Nebraska vs. MD distinction is academic only... the kid could move to California for the rest of his life without much fanfare.
So, as a result, let's assume the parents of the Skyborn actually live in New York. Then te kid gets registered as a New York Citizen, his place of birth is "Above Nebraska" (or the state's equivalent rule) on OP's hypothetical. The couple on the Lufthansa flight could ask to have Berlin (Germany) written into the record, as that is where the interior of all Lufthansa planes is to be considered under the law over international waters.