In this paper, we will study ground state sign-changing solutions for asymptotically cubic or super-cubic Schrödinger-Bopp-Podolsky systems in two situations. Firstly, we consider the following system: \(\begin{aligned}{\left\{ \begin{array}{ll}-\Delta u+V(x)u+\phi u=f(x,u), & x\in \mathbb {R}^3\\ -\Delta \phi +a^2\Delta ^2\phi =4\pi u^2, & x\in \mathbb {R}^3\end{array}\right. }\end{aligned}\) and under an appropriate assumption on V(x), we consider a weaker condition on f(x, u), which is asymptotically cubic to replace the usual super-cubic condition. In this case, we establish the existence of one radial ground state sign-changing solution \(u_\lambda \) with precisely two nodal domains. In addition, we prove that the energy of any radial sign-changing solution is strictly larger than two times the least energy. Secondly, we consider the following system which lacks compactness: \(\begin{aligned} {\left\{ \begin{array}{ll}-\Delta u+V(x)u+\phi u=K(x)f(u), & x\in \mathbb {R}^3\\ -\Delta \phi +a^2\Delta ^2\phi =4\pi u^2, & x\in \mathbb {R}^3\end{array}\right. }\end{aligned}\) where V, \(K\in \mathcal {C}(\mathbb {R}^3,\mathbb {R})\) and \(f\in \mathcal {C}(\mathbb {R},\mathbb {R})\) , and here we use a weaker growth condition of f(u). With some new tricks and inequalities, we overcome the compactness and establish the existence of one ground state sign-changing solution with precisely two nodal domains.
