A modified multiphase flow model is applied for a better understanding of bio-nanofluid (blood containing 4% (w/v) Fe3O4 nanoparticles) flow regimes through a real bifurcated artery. The magnetic field with distinct current intensities (I = 0 – 300 A) was employed to induce the flow features when the wire's source is placed nearby the junction of the asymmetrical branched artery during numerical computation. The finite volume method was used to solve the coupled hemodynamics model. Results show that the pressure, and vorticity profiles increased and fallen gradually with the existence of the magnetic source and further obtained the maximum pressure for the strong current intensity (I = 300 A). The fluctuating vorticity distributions are found along the inner and outer vessel wall as well as the predicted lines created within the simulated domain for the increase of current intensity. The velocity outlines variates steadily, and the local peak velocities are obtained with the increase of the magnetic force. With the increment of the current intensity upto I = 300 A, the flow rate rises progressively for the asymmetric branched vessel, and the opposite scenario is found for the root vessel. The temperature profiles decrease steadily with the increment of the applied current intensity. With the manifestation of the magnetic source, the irregular flow behaviours are found within the asymmetrical bifurcated artery. This modeling investigation could be beneficial for the emergent therapy plan of ample vascular diseases as the magnetic drug targeting system.