In this paper, we study the existence of normalized solutions for the fractional critical Schrödinger–Poisson system \(\begin{aligned}{\left\{ \begin{array}{ll} (-\Delta )^su +\gamma \phi u= \lambda u+\mu |u|^{q-2}u+|u|^{2^*_s-2}u,& ~~ \text{ in }~{\mathbb {R}}^3,\\ (-\Delta )^t\phi =u^2,& ~~ \text{ in }~{\mathbb {R}}^3,\end{array}\right. } \end{aligned}\) with the prescribed \(L^2\) -norm \( \int _{{\mathbb {R}}^3} |u|^2dx=a^2,\) where \( s, t \in (0, 1)\) satisfies \(2\,s+2t> 3, q\in (2,2^*_s), a>0\) and \(\gamma ,\mu >0\) are parameters. We establish several existence results for the \(L^2\) -subcritical regime, i.e., \(q \in (2,2+\frac{2(3-2t)}{3})\) ; the \(L^2\) -critical regime, i.e., \(q=2+\frac{4s}{3}\) , and the \(L^2\) -supercritical regime, i.e., \(q\in (2+\frac{4s}{3},2^*_s)\) . These cases are studied under different assumptions imposed on the parameters \(\gamma ,\mu \) and the mass a, respectively. To prove the above conclusions, we comprehensively apply the Jeanjean’s theory, Pohozaev manifold method and Brezis-Nirenberg’s technique skill to overcome the lack of compactness. This paper complements the paper by He, Meng and Squassina (Calc Var PDE, 63(6): 142, 2024); and the paper by Li and Teng (Mediterr J Math, 20(2):92, 2023), since we consider the normalized solutions of the fractional Schrödinger–Poisson problems with the Sobolev critical term, and the perturbation \(\mu |u|^{q-2}u\) is allowed to have \(L^2\) -critical growth, i.e., \(q=2+\frac{4s}{3}\) .
