In this paper, we consider the following fractional Schr\”{o}dinger-Poisson system: \begin{equation*} \left\{ \begin{array}{ll} (-\Delta)^su+u+\lambda K(x)\phi u=a(x)|u|^{p-2}u+b(x)|u|^{2}u& \hbox{in $\mathbb{R}^3$,}\\ (-\Delta)^t\phi=K(x)u^2& \hbox{in $\mathbb{R}^3$,} \end{array} \right. \end{equation*} where $s,t\in(0,1)$, $\lambda>0$, $2