From both classical and quantum aspects, the classical orbits and wave functions of a charged particle motion are investigated in two-dimensional central-scalar-potential as well as the gauge field of a magnetic flux multi-connected space. The result shows that the spatial patterns of the probability clouds of wave functions are in excellent agreement with classical orbits. Moreover, fractional quantization rule of angular momentum may be uniquely determined by quantum-classical correspondence. The gauge potential of a magnetic flux cannot change the quantization rule but results in a common topological phase for all wave functions in the given model.