In this article, we deal with the nonlinear Schrödinger equation with nonlocal regional diffusion 0.1 (Formula presented.) where 0 < ? < 1, n ? 2, and (Formula presented.) is a continuous function. The operator (Formula presented.) is a variational version of the nonlocal regional Laplacian defined as (Formula presented.) where (Formula presented.) be a positive function. Considering that ?, V, and f(·, t) are periodic or asymptotically periodic at infinity, we prove the existence of ground state solution of (1) by using Nehari manifold and comparison method. Furthermore, in the periodic case, by combining deformation-type arguments and Lusternik–Schnirelmann theory, we prove that problem (1) admits infinitely many geometrically distinct solutions. © 2020 John Wiley & Sons, Ltd.