  We deal with the existence of positive solutions for the following fractional
Schr\"odinger equation $$ \varepsilon ^{2s} (-\Delta)^{s} u + V(x) u = f(u)
\mbox{ in } \mathbb{R}^{N}, $$ where $\varepsilon>0$ is a parameter, $s\in (0,
1)$, $N>2s$, $(-\Delta)^{s}$ is the fractional Laplacian operator, and
$V:\mathbb{R}^{N}\rightarrow \mathbb{R}$ is a continuous positive function.
Under the assumptions that the nonlinearity $f$ is either asymptotically linear
or superlinear at infinity, we prove the existence of a family of positive
solutions which concentrates at a local minimum of $V$ as $\varepsilon$ tends
to zero.
