Magnetic field is a favorable power source for actuation and control of micro-/nanorobots. To overcome the fast decay of magnetic field for large-workspace microrobotic actuation, mobile field source-based systems have been proposed. In this work, we report a new mobile-coil system, i.e., QuadMag. It consists of four electromagnetic coils, whose motion is actuated by a parallel mechanism. Compared to previous systems with three mobile coils, e.g., DeltaMag, the additional coil in the QuadMag increases the degree-of-freedom (DoF) for magnetic control. However, to control QuadMag, new control methods should be developed for the over-constrained parallel mechanism and for the field/force of the four coils. We derive the Jacobian matrix for the differential motion of the parallel mechanism and then formulate the field, force and simultaneous field and force control methods for magnetic actuation. Comparative experiments validate the enhanced actuation efficiency when controlling torque-driven helical microrobots. Moreover, the magnetic actuation dexterity is also enhanced by the additional coil. We conduct simulated navigation experiments and prove the actuation capability of QuadMag for 3D force-driven microrobot navigation with controlled robot orientation.