  We study the following fractional Schr\"{o}dinger equation
\begin{equation*}\label{eq0.1} \epsilon^{2s}(-\Delta)^s u + V(x)u = |u|^{p -
2}u, \,\,x\in\,\,\mathbb{R}^N, \end{equation*} where $s\in (0,\,1)$, $N>2s$,
$p>1$ is subcritical and $V(x)$ is a nonnegative continuous potential. We use
penalized technique to show that the problem has a family of solutions
concentrating at a positive local minimum of $V(x)$ provided that
$\frac{2s}{N-2s}+2<p<\frac{2N}{N-2s}$. The novelty is that $V$ can decay
arbitrarily or even be compactly supported.
