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A small spherical rigid particle in a cylindrical cavity is considered. The harmonic rotation of the cavity wall drives the background flow characterized by the Strouhal number Str, assumed as the first parameter of our investigation. The particle immersed in the flow (assumed Stokesian) has a Stokes number St=1 and a particle-to-fluid density ratio ϱ which is assumed as the second parameter of this study. Building on the theoretical understanding of the recently discovered oscillatory switching centrifugation for inertial particles in unbounded flows, we investigate the effect of a confinement. For the first time we study how the presence of a wall affects the particle trajectory in oscillatory switching centrifugation dynamics. The emergence of two qualitatively different particle attractors is characterized for particles centrifuged towards the cavity wall. The implication of two such classes of attractors is discussed focusing on the application to microfluidics. We propose some strategies for exploiting the confined oscillatory switching centrifugation for selective particle segregation and for the enhancement of particle interaction events.