In this manuscript, what we believe to be a novel hyperbolic-graded topological nano-photonic resonator structure is proposed to excite robust topological edge states. The graded refractive index is realized by considering a porous silicon material having a deliberately modulated local refractive index. The introduction of grading effectively modifies its dispersion characteristics leading to distinctive topological properties. This results in excitation of a topologically protected edge state (TES) having significantly higher interface electric field intensity at an operational wavelength of 1521 nm. Additionally, the impact of interface layer thicknesses on the excitation of these TES is thoroughly investigated. Finally, the structure's capability to be used as a refractive index sensor is also demonstrated. The analytical results demonstrate an average sensitivity of 852.14 nm/RIU, coupled with a quality factor of 4019.23 and a figure of merit (FOM) of 1277.13 RIU-1. With its remarkable performance metrics, the proposed device holds significant promise for accurately detecting and sensing biochemical samples with very high efficiency.