In Windows platform, I can use the statements:
format PE console
include 'win32a.inc' ; Already added as an environment path

But in GNU/Linux when I try the above code segment, and run using the terminal, I get an error as 'win32a.inc' not found. Is there a way I can generate .exe in GNU/Linux with no errors? I am a 19 year old x86 programmer. Sorry in advance if my query is out of scope.

Yes.

You can add/copy the files from the windows download into a folder in your PATH in Linux.

Make sure that that capitalisation matches exactly in Linux. In Windows this is not checked, but Linux requires it to match..

Try running the Win32 version of FASM on Linux with WINE.

I don't want to use wine, I want to use the "apt-get install fasm" version. Can anyone provide a reply as what I should write instead of "include win32a.inc" in order to generate an executable using GNU/Linux?

You don't need to write anything different. What you need is to have the file win32a.inc, and the other windows header files, in your INCLUDE path.