We numerically investigate the motion of stars on the meridional plane of an axially symmetric disk galaxy model, containing a central supermassive black hole, represented by the Paczynski-Wiita potential. By using this pseudo-Newtonian potential we can replicate important relativistic properties, such as the existence of the Schwarzschild radius. After classifying extensive samples of initial conditions of trajectories, we manage to distinguish between collisional, ordered, and chaotic motion. Besides, all starting conditions of regular orbits are further classified into families of regular orbits. Our results are presented through modern color-coded basin diagrams on several types of two-dimensional planes. Our analysis reveals that both the mass of the black hole (in direct relation with the Schwarzschild radius) as well as the angular momentum play an important role in the character of orbits of stars. More specifically, the trajectories of low angular momentum stars are highly affected by the mass of the black hole, while high angular momentum stars seem to be unaffected by the central black hole. Comparison with previous related outcomes, using Newtonian potentials for the central region of the galaxy, is also made.