Matter is defined as anything that occupies space and has mass,so i was wondering whether it was possible for anything to occupy space and not have mass or for something to have mass but not occupy any space?

It is not possible for something to occupy space and not have mass or for something to have mass but not occupy any space and be called as 'matter'. It is against the fundamentals of physics as matter is something that occupies space and has mass.

Also, anything that would have had mass but would occupy no space, would have infinite density.