This scientific article presents an innovative plasmonic filtering device featuring a distinctive geometric configuration, characterized by the rectangular ring resonator made from graphene, which includes two narrow gaps. This unique design facilitates dynamic control over the working frequency range and the transmission peak frequency. By carefully adjusting the width of the graphene nanoribbons and manipulating the coupling distance between the waveguide and the resonator, the device allows for precise modifications of its operational characteristics. The filter is designed to operate in a single-mode capacity, showcasing exceptional frequency response performance. Furthermore, one of its noteworthy attributes is its sensitivity to variations in surrounding mediums, positioning it as a promising candidate for advanced biosensor applications that require high responsiveness. This novel structure not only contributes to the miniaturization of plasmonic filtering devices but also holds the potential for seamless integration into compact plasmonic circuitry. In summary, when compared to various other structures, the proposed design stands out due to its minimized dimensions, single-mode functionality, and superior frequency response capabilities, making it a significant advancement in the field.