The dispersion properties of electrostatic surface waves propagating along the interface between a quantum magnetoplasma, composed of electrons and positrons, and vacuum axe studied by using a quantum magnetohydrodynamic plasma model. The general dispersion relation for arbitrary orientation of Me magnetic field and the propagation vector 4 derived and analyzed in some special cases of interest (viz. when be magnetic field is directed parallel and perpendicular to the boundary surface). It is found that the quantum effects facilitate the propagation of electrostatic surface modes in a dense magnetoplasma. The effect of the external magnetic field is found to increase the frequency of be quantum surface wave. The existence of a singular wave on the boundary surface is also proved, and its properties axe analyzed numerically. It is shown that the new wave characteristics appear due to the Rayleigh type of the wave.