Electron has volume or not?
If volume is understood classically, i.e. as the quantity of three-dimensional space enclosed by a closed surface, then quantum systems in general do not have a certain volume. One could, in principle, redefine the notion of volume for a quantum system to be, say, an area chosen so that there is a certain probability (for example, 90%) of finding the system within it, but that would be a completely different quantity, of course. It should also be noted that in quantum theory statements about a system having or possessing certain values of physical quantities has a lot of issues, even when the quantities are well defined. For instance, does a quantum system have (possess) certain values for physical quantities before the corresponding measurements are made?


  On other hand In general Chemistry books often spin quantum no. is
  referred as electron spinning on its axis.


You already know that such picture is an absurd, and you are perfectly right here: electrons are not spinning. So there is no any contradiction there: they don't have a classical volume and they are not spinning.