We report the effects of the magnetic field on resistive switching behavior in the Ag / BiFeO 3 / FTO RRAM device through conventional I-V characteristics. The switching of the device from a high resistance state (HRS) to a low resistance state (LRS) at a certain threshold voltage (Vt) evidences a shift under the magnetic influence. The shifting of Vt toward higher voltage is due to the appearance of the Lorentz force and magnetoelectric effect when the magnetic field is applied perpendicular to the flow of current. The resistance of the HRS and LRS increases simultaneously under the application of the magnetic field due to the induced Hall resistance effect. The OFF / O N ratio ∼ 12, which is repeatable for 100 multiple cycles. The discrete RESET state of the device is achieved by pulse-width and pulse-height modulation. Substantially, the resistance of these states increases systematically under the action of the magnetic field. The control of resistance states with the pulse-height and magnetic field in Ag / BiFeO 3 / FTO shows promise for future multilevel non-volatile memory technology. © 2020 Author(s).