There isn’t at least directly above the country. This normally applies to all countries as well.

At certain heights you are in space and space is international. Anything above 110km is normally considered space, anything below 60km is a country's air space, anything between is a grey area.

That's why the gean BND had it's Space theory to justify it's spying.

The chinese was way below that a ca. 19km

I’d say it’s best to think of that gray zone as more of a nobody really operates here zone.

"According to international law, states retain sovereignty over the airspace above their territory – subject to certain aviation laws such as the 1944 Convention on International Civil Aviation (the Chicago Convention). Article 1 of the Chicago Convention makes this clear by providing that every state has complete and exclusive sovereignty over the airspace above its territory.

This exclusive sovereignty does not extend to space, because according to Article 2 of the Outer Space Treaty, outer space is not subject to national appropriation by claim of sovereignty, by means of use or occupation, or by any other means.

But where does sovereignty over airspace stop, and outer space begin? The exact legal boundary of space is not defined in international law."

https://commonslibrary.parliament.uk/research-briefings/cbp-....

So No, but Yes eventually there is a limit ...

I think it's uncontroversial that FL600 (60K feet MSL) is not "space".

The US is a signatory to the Outer Space Treaty, which stipulates that signatories make no territorial claims to outer space. The definition of outer space is often taken to be the Kármán line at 100km. However, the Treaty doesn't use any particular definition. But it does specify that the Moon is part of outer space. So we can assume the US is no taller than 362600km.