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$\\ \\ x\\in \\mathbb{R}^N,$ where $ u(x) \\rightarrow 0$ as $|x| \\rightarrow \\infty,$ and $(-\\Delta)_{A_\\varepsilon}^s$ is the fractional magnetic operator with $0<s<1$, $2_s^\\ast = 2N/(N-2s),$ $M : \\mathbb{R}^{+}_{0} \\rightarrow \\mathbb{R}^{+}$ is a continuous nondecreasing function, $V:\\mathbb{R}^N \\rightarrow \\mathbb{R}^+_0,$ and $A: \\mathbb{R}^N \\rightarrow 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