We investigate the existence of normalized solutions for the following nonlinear fractional Choquard equation: \(\begin{aligned} (-\Delta )^s u+V(\epsilon x)u=\lambda u+\left( I_\alpha *|u|^q\right) |u|^{q-2} u+\left( I_\alpha *|u|^p\right) |u|^{p-2} u, \ x \in {\mathbb {R}}^N, \end{aligned}\) subject to the constraint \(\begin{aligned} \int _{{\mathbb {R}}^N}|u|^2 \textrm{d}x=a>0, \end{aligned}\) where \(N>2 s, s \in (0,1), \alpha \in (0, N), \frac{N+\alpha }{N}<q<\frac{N+2 s+\alpha }{N}<p\le \frac{N+\alpha }{N-2 s}\) , \(\epsilon >0\) is a parameter, and \(\lambda \in {\mathbb {R}}\) serves as an unknown parameter acting as a Lagrange multiplier. By employing the Lusternik-Schnirelmann category theory, we estimate the number of normalized solutions to this problem by virtue of the category of the set of minimum points of the potential function V.
