The effects of an externally applied one-dimensional periodic potential on the freezing and melting behavior of two-dimensional systems of colloidal particles with a short-range attractive interaction are studied using Monte Carlo simulations. In such systems, incommensuration results when the periodicity of the external potential does not match the length scale at which the minimum of the attractive potential occurs. To study the effects of this incommensuration, we consider two different models for the system. Our simulations for both these models show the phenomenon of reentrant freezing as the strength of the periodic potential is varied. Our simulations also show that different exotic phases can form when the strength of the periodic potential is high, depending on the length scale at which the minimum of the attractive pair potential occurs.