In this paper, we consider the following fractional Schrödinger equation with singular potential and Hartree-type nonlinearity \(\begin{aligned} \left\{ \begin{array}{l} (-\varDelta )^s u-\frac{u}{|x|^\theta }-\mu |u|^{q-2} u-\eta \left( I_\alpha *h|u|^{2_\alpha }\right) h|u|^{2_\alpha -2} u-\lambda u=0 \; \text{ in } \mathbb {R}^N, \int _{\mathbb {R}^N}u^2 d x=c, \end{array}\right. \end{aligned}\) where \(s \in \left( \frac{1}{2}, 1\right) , \mu \geqslant 0, c>0, N \geqslant 3,0<\theta <2 s\) , \(2<q<2+\frac{4 s}{N}, 2_\alpha :=\frac{N+\alpha }{N}\) , \(\alpha \in (0, N), h: \mathbb {R}^N \rightarrow (0, \infty )\) is a continuous function and \(\lambda \in \mathbb {R}\) is an unknown Lagrange multiplier. We not only concern with the existence of normalized ground state solutions for the above problem for cases \(\mu =\eta =0\) , but also investigate the existence and asymptotic behavior of normalized ground state solutions to the above problem under reasonable assumptions on h(x) for cases \(\mu >0\) and \(\eta =1\) .
