We present a theoretical study of the one-electron states of a semiconductor-made quantum ring (QR) containing a series of piecewise-constant wells and barriers distributed along the ring circumference. The single quantum well and the superlattice cases are considered in detail. We also investigate how such confining potentials affect the Aharonov–Bohm like oscillations of the energy spectrum and current in the presence of a magnetic field. The model is simple enough so as to allow obtaining various analytical or quasi-analytical results. We show that the well-in-a-ring structure presents enhanced localization features, as well as specific geometrical resonances in its above-barrier spectrum. We stress that the superlattice-in-a-ring structure allows giving a physical meaning to the often used but usually artificial Born–von-Karman periodic conditions, and discuss in detail the formation of energy minibands and minigaps for the circumferential motion, as well as several properties of the superlattice eigenstates in the presence of the magnetic field. We obtain that the Aharonov–Bohm oscillations of below-barrier miniband states are reinforced, owing to the important tunnel coupling between neighbour wells of the superlattice, which permits the electron to move in the ring. Additionally, we analysis a superlattice-like structure made of a regular distribution of ionized impurities placed around the QR, a system that may implement the superlattice in a ring idea. Finally, we consider several random disorder models, in order to study roughness disorder and to tackle the robustness of some results against deviations from the ideally nanostructured ring system.