A white dwarf model with cylindrical symmetry is used to investigate the effect of a uniform vertical magnetic field on the periods of g-modes trapped in the compositionally stratified surface layers. For those modes for which trapping is most effective, the periods wander by approximately 10% about their zero-field values as B0 increases. As the field strength increases further, the period may abruptly increase by some 25% to a new, more stable value; see Figure 1. The periods of less efficiently trapped modes do not show this sensitivity for field strengths up to 1 MG, the upper limit examined.