We study convection in a vertical layer of ferro-magnetic fluid heated from the side and subject to a transverse magnetic field. It is found that the subse- quent fluid motion is caused by interacting thermo-gravitational and thermo- magnetic mechanisms. Our experiments and computations show that the excitation of magneto-convection leads to the formation of vertically aligned stationary rolls, while gravitational convection results in horizontal rolls cor- responding to a pair of counter-propagating thermal waves. The interaction of these instability modes leads to a wide spectrum of experimentally observed flow patterns including stationary rolls and standing waves of various spatial orientations. A comprehensive stability map is computed and compared with experimental flow visualisations. Disturbance energy is analysed to achieve a deeper insight into the physical mechanisms driving the fluid motion.