  We study the following fractional Schr\"{o}dinger equation
\begin{equation}\label{eq0.1} \varepsilon^{2s}(-\Delta)^s u + Vu = |u|^{p -
2}u,\ \ x\in\,\,\mathbb{R}^N. \end{equation} We show that if the external
potential $V\in C(\mathbb{R}^N;[0,\infty))$ has a local minimum and $p\in (2 +
2s/(N - 2s), 2^*_s)$, where $2^*_s=2N/(N-2s),\,N\ge 2s$, the problem has a
family of solutions concentrating at the local minimum of $V$ provided that
$\liminf_{|x|\to \infty}V(x)|x|^{2s} > 0$. The proof is based on variational
methods and penalized technique.
  {\textbf {Key words}: } fractional Schr\"{o}dinger; vanishing potential;
penalized technique; variational methods.
