We consider a class of relativistic quantum systems of ring geometry with mass confinement, subject to a magnetic flux. Such a system supports a family of boundary modes with edge-dependent currents and spin polarization as the spinor-wave analog of the whispering-gallery modes. While these states are remarkably robust against random scattering, boundary deformations and/or bulk disorders can couple the two oppositely circulating base states. Superposition of the two states can be realized by sweeping an external magnetic flux. We also address the issue of decoherence and articulate a possible experimental scheme based on 3D topological insulators.