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Direct $CP$ asymmetries (${\mathcal{A}}_{CP}$) in the inclusive decays of $\overline{B}\ensuremath{\rightarrow}{X}_{s}\ensuremath{\gamma}$ and $\overline{B}\ensuremath{\rightarrow}{X}_{s+d}\ensuremath{\gamma}$ order 1% will be probed at BELLE II experiment. In this work, three such are studied context a three-Higgs-doublet model (3HDM), it is shown that all ${\mathcal{A}}_{CP}$ can as large current experimental limits. Of particular interest for $\overline{B}\ensuremath{\rightarrow}{X}_{s+d}\ensuremath{\gamma}$, which predicted to effectively zero Standard Model (SM). A measurement 2.5% or more observable with full data would give $5\ensuremath{\sigma}$ evidence physics beyond SM. We display parameter space 3HDM clear signal possible.