This paper is devoted to the following fractional Schrödinger-Poisson
systems: \begin{equation*}
\left\{\aligned
&(-\Delta)^{s} u+V(x)u+\phi(x)u=
f(x,u)
\,\,\,&\text{in
} \mathbb{R}^3, \\ &
(-\Delta)^{t} \phi(x)=u^2
\,\,\,&\text{in
} \mathbb{R}^3, \endaligned
\right. \end{equation*} where
$(-\Delta)^{s}$ is the fractional Lapalcian, $s,
t \in (0, 1),$ $V : \R^3
\to \R$ is continuous. In contrast to
most studies, we consider that the potentials $V$ is indefinite. With
the help of Morse theory, the existence of nontrivial solutions for the
above problem is obtained.