  We investigate the properties of electron states localized at the edge of a
superconducting island placed on the surface of a topological insulator in a
magnetic field. In such systems, Majorana fermions emerge if an odd number of
vortices (or odd multivortex vorticity) is hosted by the island; otherwise, no
Majorana states exist. Majorana states emerge in pairs: one state is localized
near the vortex core, and another at the island edge. We analyze in detail the
robustness of Majorana fermions at the edge of the island threaded by a single
vortex. If the system parameters are optimized, the energy gap between the
Majorana fermion and the first excited state at the edge is of the order of the
superconducting gap induced on the surface of the topological insulator. The
stability of the Majorana fermion state against a variation of the gate voltage
and its sensitivity to the magnetic field allows one to distinguish
experimentally the edge Majorana fermion from conventional Dirac fermions.
