We propose and investigate a graphene periodic subsurface structure consisting of a coplanar pair of ring resonators and a ribbon. The Fano-like interference can be actively regulated by the applied magnetic field, incident angle and Fermi energy. Since the excited charges of graphene monolayer have cyclotron properties in the external magnetic field, the transmittance and line-shape can be effectively controlled. At a certain frequency, different magnetic fields have different effects on the conductivity tensor of graphene, which affects the metallic properties of graphene, leading to changes in the transmittance. The Fano-like line-shape can be regulated by adjusting the incident angle to delay the phase between adjacent graphene sheets. In addition, the resonance frequency can be electrically regulated through Fermi energy. Finite element method (FEM) is introduced to analyze the graphene periodic structure and the results are demonstrated by multimode interference coupled mode theory (MICMT). The Faraday rotation angle exceeding 85o are observed in a small magnetic flux density B of about 0.5T. Moreover, a high ON/OFF ratio plasma-optic switching is designed, and the ON/OFF ratio (η) of the switch is 19.921dB. Notably, combining the influence of magnetic flux density on transmittance and the modulation of resonance frequency by Fermi energy, optical switching can be implemented at any frequency within the frequency range studied. These results provide methods for active regulation of electromagnetic waves in the terahertz field and have potential applications in optical switching and integrated photonic circuit.