Recently, high-order topological photonic crystals (PhCs) have attracted huge research attention due to their novel physics mechanism and the application potential in integrated photonics. Based on the two-dimensional Su-Schrieffer-Heeger model, we construct and study the mutual coupling between the high-order corner states in 2D dielectric PhCs. Simulation results show that the Q-factor of such corner-localized quasi-bound states in the continuum (BICs) could be enhanced following mutual coupling in finite size. Furthermore, we study the side-coupled structure based on defect-hybrid waveguides and the edge state microring, the quasi-BIC microcavity. The refractive index sensing application based on corner-localized quasi-BICs shows outstanding simulated sensitivity (312.8 nm/RIU) and figure of merit (∼103 1/RIU). The robustness against fabrication errors due to its topologically protected nature makes it competitive compared with other quasi-BICs sensors.