In this work, the spectra in an Aharonov–Bohm quantum-ring interferometer forming a Josephson junction between two topological superconductor (TSC) nanowires are investigated. The TSCs host Majorana bound states at their edges, and both the magnetic flux and the superconducting phase difference between the TSCs are used as control parameters. A tight-binding approach is used to model the quantum ring coupled to both TSCs, described by the Kitaev effective Hamiltonian. The problem is solved by means of exact numerical diagonalization of the Bogoliubov-de Gennes Hamiltonian and obtain the spectra for two sizes of the quantum ring as a function of the magnetic flux and the phase difference between the TSCs. Depending on the size of the quantum ring and the coupling, the spectra display several patterns. Those are denoted as line, point, and undulated nodes, together with flat bands, which are topologically protected. The first three patterns can be possibly detected by means of persistent and Josephson currents. Hence, the results could be useful to understand the spectra and their relation with the behavior of the current signals.