If you have the command line tools installed, it should also be under /Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/usr/include/sys/syscall.h. macOS, by default, does not ship with these headers at all, and as of macOS Mojave they no longer provide them under /usr/include unless you install a certain package.

With that being said, I disagree with your characterization of “some header”–anything that’s in Apple’s headers is public API, whether it has a fancy page on developer.apple.com or not. Apple has a very clear definition of what they consider to be “private”, and anything in /usr/include isn’t it.

Actually the path is:

  /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX.sdk/usr/include/sys/syscall.h 

and you can clearly see that the file is wrapped with:

  #ifdef __APPLE_API_PRIVATE
  ...
  #endif /* __APPLE_API_PRIVATE */

Again, if you have the Command Line Tools installed, it'll be under /Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/. Xcode also has a copy, but I think fewer people have that installed.

Nope, on my system, without xcode, the previous poster's path is correct: /Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/usr/include/sys/syscall.h