  This paper focuses on the following class of fractional magnetic
Schr\"{o}dinger equations \begin{equation*}
  (-\Delta)_{A}^{s}u+V(x)u=g(\vert u\vert^{2})u+\lambda\vert u\vert^{q-2}u,
\quad \mbox{in } \mathbb{R}^{N}, \end{equation*} where $(-\Delta)_{A}^{s}$ is
the fractional magnetic Laplacian, $A :\mathbb{R}^N \rightarrow \mathbb{R}^N$
is the magnetic potential, $s\in (0,1)$, $N>2s$, $\lambda \geq0$ is a
parameter, $V:\mathbb{R}^N \rightarrow \mathbb{R}$ is a potential function that
may decay to zero at infinity and $g: \mathbb{R}_{+} \rightarrow \mathbb{R}$ is
a continuous function with subcritical growth. We deal with supercritical case
$q\geq 2^*_s:=2N/(N-2s)$. Our approach is based on variational methods combined
with penalization technique and $L^{\infty}$-estimates.
