In this paper, we study the following fractional Schrödinger equation with electromagnetic fields and critical or supercritical growth (-Δ)Asu+V(x)u=λ|u|p-2u+f(x,|u|2)u,x∈RN,\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} (-\Delta )_A^su+V(x)u=\lambda |u|^{p-2}u+ f(x,|u|^2)u, \ x \in \mathbb {R}^N, \end{aligned}$$\end{document}where (-Δ)As\documentclass[12pt]{minimal}
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\begin{document}$$(-\Delta )_A^s$$\end{document} is the fractional magnetic operator with 0<s<1\documentclass[12pt]{minimal}
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\begin{document}$$0<s<1$$\end{document}, N>2s\documentclass[12pt]{minimal}
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\begin{document}$$N>2s$$\end{document}, 2s∗=2NN-2s\documentclass[12pt]{minimal}
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\begin{document}$$2_s^*=\frac{2N}{N-2s}$$\end{document}, λ>0\documentclass[12pt]{minimal}
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\begin{document}$$\lambda >0$$\end{document}, V∈C(RN,R)\documentclass[12pt]{minimal}
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\begin{document}$$V \in C(\mathbb {R}^N,\mathbb {R})$$\end{document} and A∈C(RN,RN)\documentclass[12pt]{minimal}
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\begin{document}$$A \in C(\mathbb {R}^N, \mathbb {R}^N)$$\end{document} are the electric and magnetic potentials, respectively. When V and f are asymptotically periodic in x, and f is a continuous function and there exists 2<q<2s∗\documentclass[12pt]{minimal}
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\begin{document}$$2< q<2_s^*$$\end{document} such that |f(x,t)|≤C(1+|t|q-22)\documentclass[12pt]{minimal}
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\begin{document}$$|f(x,t)|\le C(1+|t|^{\frac{q-2}{2}})$$\end{document} for all (x, t), for 2s∗≤p<22s∗-q\documentclass[12pt]{minimal}
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\begin{document}$$ 2_s^*\le p<22^{*}_{s}-q$$\end{document}. For any D>0\documentclass[12pt]{minimal}
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\begin{document}$$D>0$$\end{document} fixed, if λ∈(0,D]\documentclass[12pt]{minimal}
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\begin{document}$$\lambda \in (0,D]$$\end{document} we prove that the equation has a nontrivial solution by the truncation method. Our method can provide a prior L∞\documentclass[12pt]{minimal}
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\begin{document}$$L^{\infty }$$\end{document}-estimate.
