We show that the application of reasonably small external magnetic fields can improve the photoresponse of graphene-based field effect transistors. The proposed device is based on a disk of gated bilayer graphene, such that the drain spans its circumference and a eccentric point-like source is connected to its interior. An AC THz potential difference is applied between source and gate while a static source-drain voltage, rectified by the nonlinearities of the electron liquid, is measured. Peaks in the rectified potential occur at frequencies that enable the excitation of standing plasma waves in the device. When a magnetic field is applied perpendicular to the device, the entirety of collective plasma modes is split into bulk and edge magnetoplasmons. These two branches of the collective spectrum produce two sets of resonant peaks, which exhibit different scalings with the applied magnetic field. Similar to the effect of changing a bias voltage in a nearby gate, the peak frequency can be shifted with the external magnetic field strength. More importantly, their magnitude can be enhanced or suppressed based on their proximity to the cyclotron frequency. Therefore, it becomes possible to isolate specific frequencies, by enhancing specific peaks and suppressing all others.