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Magnetic particles confined in microchannels can be actuated to perform translation motion using a rotating magnetic field, but their actuation in such a situation is not yet well understood. Here, the actuation of a ferromagnetic particle confined in square microchannels is studied using immersed-boundary lattice Boltzmann simulations. In wide channels, when a sphere is positioned close to a side wall but away from channel corners, it experiences a modest hydrodynamic actuation force parallel to the channel walls. This force decreases as the sphere is shifted toward the bottom wall but the opposite trend is found when the channel is narrow. When the sphere is positioned midway between the top and bottom channel walls, the actuation force decreases as the channel width decreases and can reverse its direction. These phenomena are elucidated by studying the flow and pressure fields in the channel-particle system and by analyzing the viscous and pressure components of the hydrodynamic force acting on different parts of the sphere.