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Patterns formed by nano/microparticles in colloidal systems are of great interest and importance from both scientific and technological points of view. Magnetic colloids are particularly interesting since the structures formed by magnetic particles can be quite easily controlled by external magnetic fields. In this study, we investigate the growth process of clusters formed by paramagnetic microparticles in a fluctuating magnetic field composed of a direct current field applied in the vertical direction and an alternating current one in the horizontal direction. We find that thin walls, the thickness of which is equal to the diameter of a particle, are formed by paramagnetic particles; the horizontal length of the walls increases via wall-edge-to-wall-edge coagulation, but they do not grow laterally due to repulsive forces acting between walls in the lateral direction. Finally, we investigate the scaling features of the growth process of the walls. We find that a scaling law applies to the growth of the walls during a certain period of the growth process.