A refractive index sensor with a free spectral range that is unlimited by neighboring mode spacing (10 fold increase with respect to 20 nm of an unmodified ring), based on an optical silicon-on-insulator microring resonator patterned with periodically arranged set of gold nanodisks, is presented and numerically verified. It is shown that the particular periodic arrangement of nanodisks selects a single resonance from a wide set of ring resonator modes and removes mode splitting. Extraction of the waveguided electromagnetic energy into evanescent plasmonic modes enhances light-analyte interaction and increases device sensitivity to variation of refractive index up to 176 nm/RIU (about 2-fold increase compared to the unmodified ring), which is useful for sensor applications. Proof of the concept is presented by finite-difference time-domain simulations of a design readily practicable by means of modern nanotechnology.