We consider a class of random light beams, which are generated by inserting an asymmetric Schell-model beam into a wavefront-folding interferometer. Typical propagation behavior of such optical beams modulated by several legitimate complex coherence states has been investigated. In certain cases, these beams exhibit novel rotationally symmetric intensity patterns with rectangular or lattice-like lobes, and the pattern and location of each lobe can be controlled by adjusting the source coherence parameters. Besides, beam characteristics can be flexibly modulated by varying the phase delay between the two paths of the interferometer. Our results may be applied in free-space optical communication.