We intend to study a class of the critical Schrödinger–Bopp–Podolsky system with $p$-Laplacian in ${\mathbb{R}}^3$. Under different perturbation terms, the existence and multiplicity of nontrivial solutions are obtained by using critical point theorem. Considering the influence of the $p$-Laplacian operator and critical and nonlocal terms, which cause the loss of the compactness condition, we attempt to address this difficulty by using the concentration-compactness principle and some clever analysis.