In this paper, we study the existence and concentration phenomena of solutions for the following non-local regional Schrödinger equation where I is a positive parameter, 0 < α < 1, <![CDATA[1<p, n > 2α; (-Δ)ρ α is a variational version of the regional fractional Laplacian, whose range of scope is a ball with radius ρ(x) > 0, ρ, Q, K are competing functions.