  The paper is devoted to the study of a singularly perturbed fractional
Schr\"{o}dinger equations involving critical frequency and critical growth in
the presence of a magnetic field. By using variational methods, we obtain the
existence of mountain pass solutions $u_{\varepsilon}$ which tend to the
trivial solution as $\varepsilon\rightarrow0$. Moreover, we get infinitely many
solutions and sign-changing solutions for the problem in absence of magnetic
effects under some extra assumptions.
