  In this paper, we study the existence of localized sign-changing (or nodal)
solutions for the following nonlinear Schr\"odinger-Poisson system
\begin{equation*} \begin{cases} -\varepsilon^2 \Delta u+V(x)u+\phi
u=K(x)f(u),&\text{in}~\mathbb{R}^3,\\ -\varepsilon^2 \Delta
\phi=u^2,&\text{in}~ \mathbb{R}^3, \end{cases} \end{equation*} where
$\varepsilon>0$ is small parameters, the linear potential $V$ and nonlinear
potential $K$ are bounded and bounded away from zero. By using the penalization
method together with the method of invariant sets of descending flow, we
establish the existence of an infinite sequence of localized sign-changing
solutions which are higher topological type solutions given by the minimax
characterization of the symmetric mountain pass theorem and we determine a
concrete set as the concentration position of these sign-changing solutions.
For single potential, that is, linear potential $V$ or nonlinear potential $K$
is a positive constant, we prove that these localized sign-changing solutions
concentrated near a local minimum set of the potential $V$ or a local maximum
set of the potential $K$. Moreover, our method is works for the following
nonlinear Schr\"odinger equation \begin{equation*} -\varepsilon^2 \Delta
u+V(x)u=K(x)f(u),~\text{in}~\mathbb{R}^N \end{equation*} where $N\geq 2$. The
result generalizes the result by Chen and Wang (Calc.Var.Partial Differential
Equations 56:1-26, 2017).
