<p>The aim of this article is to explore the motion of an infinitesimal body (third body) in the vicinity of the out-of-plane equilibrium points of the restricted three-body problem under the effect of continuation fraction and radiation pressure perturbations. We investigate the effect of the radiation factor of the bigger primary and continuation fraction parameter of the smaller primary on the existence, position, zero-velocity curves and stability of the out-of-plane equilibrium points. It is discovered that the presence of these points is made possible by the bigger primary’s radiation. These equilibria arise in symmetric pair, and their number may be zero or two based on the values of the radiation and mass ratio parameters. Our results reveal that all the involved parameters have strong influence on the position of the out-of-plane equilibrium points. A numerical investigation found that the perturbing parameters have impact on the geometry of the zero-velocity curves. The stability of these points is studied in the linear sense. A detailed numerical investigation found that the equilibrium points are unstable in general.</p>