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A<sc>bstract</sc> A search for the fully reconstructed$$ {B}_s^0 $$ $B_s^0$→ μ⁺μ⁻γdecay is performed at the LHCb experiment using proton-proton collisions at$$ \sqrt{s} $$ $\sqrt{s}$= 13 TeV corresponding to an integrated luminosity of 5.4 fb⁻¹. No significant signal is found and upper limits on the branching fraction in intervals of the dimuon mass are set$$ {\displaystyle \begin{array}{cc}\mathcal{B}\left({B}_s^0\to {\mu}^{+}{\mu}^{-}\gamma \right)<4.2\times {10}^{-8},& m\left({\mu}^{+}{\mu}^{-}\right)\in \left[2{m}_{\mu },1.70\right]\textrm{GeV}/{c}^2,\\ {}\mathcal{B}\left({B}_s^0\to {\mu}^{+}{\mu}^{-}\gamma \right)<7.7\times {10}^{-8},&\ m\left({\mu}^{+}{\mu}^{-}\right)\in \left[\textrm{1.70,2.88}\right]\textrm{GeV}/{c}^2,\\ {}\mathcal{B}\left({B}_s^0\to {\mu}^{+}{\mu}^{-}\gamma \right)<4.2\times {10}^{-8},& m\left({\mu}^{+}{\mu}^{-}\right)\in \left[3.92,{m}_{B_s^0}\right]\textrm{GeV}/{c}^2,\end{array}} $$ $\begin{array}{cc}B\left(B_s^0\to {\mu }^{+}{\mu }^{-}\gamma \right)<4.2\times {10}^{-8},& m\left({\mu }^{+}{\mu }^{-}\right)\in \left(2m_{\mu },1.70\right)\mathrm{GeV}/c^2,\\ B\left(B_s^0\to {\mu }^{+}{\mu }^{-}\gamma \right)<7.7\times {10}^{-8},& m\left({\mu }^{+}{\mu }^{-}\right)\in \left(\mathrm{1.70,\; 2.88}\right)\mathrm{GeV}/c^2,\\ B\left(B_s^0\to {\mu }^{+}{\mu }^{-}\gamma \right)<4.2\times {10}^{-8},& m\left({\mu }^{+}{\mu }^{-}\right)\in \left(3.92,m_{B_s^0}\right)\mathrm{GeV}/c^2,\end{array}$ at 95% confidence level. Additionally, upper limits are set on the branching fraction in the [2m_μ,1.70] GeV/c²dimuon mass region excluding the contribution from the intermediateϕ(1020) meson, and in the region combining all dimuon-mass intervals.