Do psychologists study about father-son relationship?

Yes, not as a major course though. Relationships in general are at the core of psychological studies. Theories dealing with the father and son relationship are usually studies as part of the psychodynamic approach, where the father figure (but most importantly the mother) plays a crucial role in the development of the so-called "ego". It's interesting reading it, a little difficult to make sense of it all initially, but it eventually does make sense.