This is one of those things that is very counterintuitive. Subatomic particles aren’t really particles the way you might think of say a marble.
They’re kindof like clouds that are denser near the middle, except they can overlap without mixing. Its super hard to visualize because at anything but the smallest scale they really do look like points. And when they interact with things they also act like points while still also acting like clouds.
A lot of people end up just giving up on trying to visualize it and just trust the math.
Enter the concept of the zero point field. For funny thermodynamic reasons no point in space can ever be at zero energy. So as for what exists in the space between particles your answer is more or less the overlapping outer portions of all those particle clouds. Along with particles that sort of pop into existence (virtual particle pairs) then disappear without ever interacting with anything else.
If you mean “is the space within an atom empty,” then the answer is no. The visual model of a nucleus orbited by electrons which would allow for the statement to make sense is a thinking tool to describe a subset of what is going on beyond what our senses can make out. There are other things happening which that model doesn’t describe.
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