An improved measurement of the decay $B_s^0\to {\mu }^{+}{\mu }^{-}$ and searches for the decays $B^0\to {\mu }^{+}{\mu }^{-}$ and $B_s^0\to {\mu }^{+}{\mu }^{-}\gamma$ are performed at the LHCb experiment using data collected in proton-proton collisions at $\sqrt{s}=7$, 8 and 13 TeV, corresponding to integrated luminosities of 1, 2 and $6{\mathrm{fb}}^{-1}$, respectively. The $B_s^0\to {\mu }^{+}{\mu }^{-}$ branching fraction and effective lifetime are measured to be $B\left(B_s^0\to {\mu }^{+}{\mu }^{-}\right)=\left(3.09_{-0.43-0.11}^{+0.46+0.15}\right)\times {10}^{-9}$ and $\tau \left(B_s^0\to {\mu }^{+}{\mu }^{-}\right)=(2.07\pm 0.29\pm 0.03)\mathrm{ps}$, respectively, where the uncertainties include both statistical and systematic contributions. No significant signal for $B^0\to {\mu }^{+}{\mu }^{-}$ and $B_s^0\to {\mu }^{+}{\mu }^{-}\gamma$ decays is found and the upper limits $B(B^0\to {\mu }^{+}{\mu }^{-})<2.6\times {10}^{-10}$ and $B(B_s^0\to {\mu }^{+}{\mu }^{-}\gamma )<2.0\times {10}^{-9}$ at 95% confidence level are determined, where the latter is limited to the range $m_{\mu \mu }>4.9\mathrm{GeV}/c^2$. Additionally, the ratio between the $B^0\to {\mu }^{+}{\mu }^{-}$ and $B_s^0\to {\mu }^{+}{\mu }^{-}$ branching fractions is measured to be $R_{{\mu }^{+}{\mu }^{-}}<0.095$ at 95% confidence level. The results are in agreement with the Standard Model predictions.