This study deals with the generalization of the Elliptic Restricted Three-Body Problem (ER3BP) by considering the effects of radiation and oblate spheroid primaries. This may illustrate a gas giant exoplanet orbiting its host star with eccentric orbit. In the three dimensional case, this generalization may possess two additional equilibrium points (L6,7, out-of-plane). We determine the existence of L6,7 in ER3BP under the effects of radiation (bigger primary) and oblateness (small primary). We analytically derive the locations of L6;7 and assume initial approximations of (μ-1, ±3A2), where  and A2 are the mass parameter and oblateness factor, respectively. The fixed locations are then determined. Our results show that the locations of L6,7 are periodic and affected by A2 and the radiation factor (q1).