The purpose of this article is to establish the multiplicity of distributional solutions to a new class of fractional Schrödinger-Poisson systems of the following form \[ \begin{cases} -div^{igma}(abla^{igma}u)+V(x)u+K(x)hi u= g(x,u) & ext{ in } \mathbb{R}^{3}, -div^{\beta}(abla^{\beta}hi) =K(x)u^{2} & ext{ in } \mathbb{R}^{3}, \end{cases} \] where $\sigma,\beta\in (0,1)$, $4\sigma+2\beta \gt 3$, and $div^{\sigma}(\nabla^{\sigma})$ denotes the distributional Riesz fractional derivative. First, we introduce the latter operator and investigate their natural functional space. Then, we pose the given problem in that space. By using variational methods, based on the symmetric mountain pass theorem under certain assumptions imposed on $g$, $K$ and $V$, we investigate the existence of infinitely many distributional solutions.