In this paper we are devoted to a time-independent fractional Schrödinger equation (−Δ)αu+V(x)u=f(x,u)in RN, where (−Δ)α stands for the fractional Laplacian of order α∈(0,1), f is either asymptotically linear or superquadratic growth. Under appropriate assumptions on V and f, we prove the existence of infinitely many nontrivial high or small energy solutions, which extend and complement previously known results in the literature.