Consider the following nonlinear Schrödinger–Bopp–Podolsky system in \(\mathbb {R}^3\) : \(\begin{aligned} {\left\{ \begin{array}{ll} -\varepsilon ^2 \Delta u + ({V + \phi }) u = u |{u}|^{p-1};\\ a^2 \Delta ^2 \phi - \Delta \phi = 4 \pi u^2, \end{array}\right. } \end{aligned}\) where \(a, \varepsilon > 0\) ; \(1< p < 5\) ; \(V :\mathbb {R}^3 \rightarrow ]{0, \infty }[\) and we want to solve for \(u, \phi :\mathbb {R}^3 \rightarrow \mathbb {R}\) . By means of Lyapunov–Schmidt reduction, we show that if \(K \ge 2\) , \(z_0\) is a strict local minimum of V, V is adequately flat in a neighborhood of \(z_0\) and \(\varepsilon \) is sufficiently small, then the system has a multipeak cluster solution with K peaks placed at the vertices of a regular convex K-gon centered at \(z_0\) .
