  We study the gauged $U(1)_{L_\mu-L_\tau}$ scotogenic model with emphasis on
latest measurement of LHCb $R_{K^{(*)}}$ anomaly and AMS-02 positron excess. In
this model, neutrino masses are induced at one-loop level with $Z_2$-odd
particles, i.e., right-handed neutrinos $N_\ell(\ell=e,\mu,\tau)$ and inert
scalar doublet $\eta$ inside the loop. Meanwhile, the gauged
$U(1)_{L_\mu-L_\tau}$ symmetry is broken spontaneously by the scalar singlet
$S$, resulting to the massive gauge boson $Z'$. Provided certain couplings to
quarks induced by heavy vector-like quarks, the gauge boson $Z'$ would
contribute to the transition $b\to s \mu^+\mu^-$, hence explain the
$R_{K^{(*)}}$ anomaly. As for the Majorana fermion DM $N$, the gauge boson $Z'$
and the singlet Higgs $H_0$ will generate various annihilation channels, among
which the $NN\to Z'Z'$ and $NN\to Z'H_0(\to Z'Z')$ channel could be used to
interpret the AMS-02 positron excess. We give a comprehensive analysis on model
parameter space with consider various current constraints. The combined
analysis shows that the $R_{K^{(*)}}$ anomaly and AMS-02 positron excess can be
explained simultaneously.

High Energy Physics - Phenomenology