A search for the decay  <math><msubsup><mi>B</mi><mi>S</mi><mn>0</mn></msubsup><mo>→</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mrow><mo>∗</mo><mn>0</mn></mrow></msup><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> $$ {B}_S^0\to {\overline{K}}^{\ast 0}{\mu}^{+}{\mu}^{-} $$ is presented using data sets corresponding to 1.0, 2.0 and 1.6 fb−1 of integrated luminosity collected during pp collisions with the LHCb experiment at centre-of-mass energies of 7, 8 and 13 TeV, respectively. An excess is found over the background-only hypothesis with a significance of 3.4 standard deviations. The branching fraction of the  <math><msubsup><mi>B</mi><mi>S</mi><mn>0</mn></msubsup><mo>→</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mrow><mo>∗</mo><mn>0</mn></mrow></msup><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> $$ {B}_S^0\to {\overline{K}}^{\ast 0}{\mu}^{+}{\mu}^{-} $$ decay is determined to be  <math><mi>ℬ</mi><mfenced><mrow><msubsup><mi>B</mi><mi>s</mi><mn>0</mn></msubsup><mo>→</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mrow><mo>∗</mo><mn>0</mn></mrow></msup><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></mrow></mfenced><mo>=</mo><mfenced><mrow><mn>2.9</mn><mo>±</mo><mn>1.0</mn><mfenced><mi>stat</mi></mfenced><mo>±</mo><mn>0.2</mn><mfenced><mi>syst</mi></mfenced><mo>±</mo><mn>0.3</mn><mfenced><mi>norm</mi></mfenced></mrow></mfenced><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>8</mn></mrow></msup></math> $$ \mathrm{\mathcal{B}}\left({B}_s^0\to {\overline{K}}^{\ast 0}{\mu}^{+}{\mu}^{-}\right)=\left[2.9\pm 1.0\left(\mathrm{stat}\right)\pm 0.2\left(\mathrm{syst}\right)\pm 0.3\left(\mathrm{norm}\right)\right]\times {10}^{-8} $$, where the first and second uncertainties are statistical and systematic, respectively. The third uncertainty is due to limited knowledge of external parameters used to normalise the branching fraction measurement.

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Evidence for the decay  <math><msubsup><mi>B</mi><mi>S</mi><mn>0</mn></msubsup><mo>→</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mrow><mo>∗</mo><mn>0</mn></mrow></msup><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> $$ {B}_S^0\to {\overline{K}}^{\ast 0}{\mu}^{+}{\mu}^{-} $$