Ownership is different from sovereignty
Sovereignty means the right and power to make and enforce laws. Ownership means having property rights over something.
Put simply, the United States (Federal and States considered collectively) has sovereignty over everything in the US (and some things outside) but everything in the US is not owned by the US. It’s owned by a bunch of different entities: individuals (US and non-US citizens), corporations (foreign and domestic), local, state and Federal governments etc.
Ownership rights are subservient to sovereignty - the government may pass a law restricting what you can do with your property because they have sovereignty over it.
Can you exert your rights to that airspace? Of course, however, the invention of aircraft required modification to the right of exclusive ownership. From United States v. Causby, 328 U.S. 256 (1946):
(a) The common law doctrine that ownership of land extends to the periphery of the universe has no place in the modern world. Pp. 328 U. S. 260-261.
(b) The air above the minimum safe altitude of flight prescribed by the Civil Aeronautics Authority is a public highway and part of the public domain, as declared by Congress in the Air Commerce Act of 1926, as amended by the Civil Aeronautics Act of 1938. Pp. 328 U. S. 260-261, 328 U. S. 266.
(c) Flights below that altitude are not within the navigable air space which Congress placed within the public domain, even though they are within the path of glide approved by the Civil Aeronautics Authority. Pp. 328 U.S. 263-264.
(d) Flights of aircraft over private land which are so low and frequent as to be a direct and immediate interference with the enjoyment and use of the land are as much an appropriation of the use of the land as a more conventional entry upon it. Pp. 328 U. S. 261-262, 328 U. S. 264-267.
This is a perfect example of the difference between ownership and sovereignty. People used to own the airspace “up to heaven” then the sovereign in the shape of the US Government changed the rules so now they don’t.
Whether you can sell the airspace above your property depends on whether the sovereign (the US) has a law that allows or prohibits the splitting of airspace rights from the underlying land. I know such a split is usually possible with water and mineral rights.
Exclusive sovereignty in the case of a Federal nation like the US means that only the Federal government has power. When only the states have power it’s called residual power and when power is shared it’s called concurrent.