We present the observation of the $\mathrm{B}^{*}_{\mathrm{s}2}(5840)^0\to\mathrm{B}^0\mathrm{K}^0_{\mathrm\scriptscriptstyle S}$ decay and the evidence for the $\mathrm{B}_{\mathrm{s}1}(5830)^0\to\mathrm{B}^{*0}\mathrm{K}^0_{\mathrm\scriptscriptstyle S}$ decay by the CMS experiment at the LHC in proton-proton collisions at $\sqrt{s}=8$\,TeV. In addition, properties of the $P$-wave $\mathrm{B}^0_\mathrm{s}$ mesons are measured, as well as the mass differences $m_{\mathrm{B}^0}-m_{\mathrm{B}^+}$ and $m_{\mathrm{B}^{*0}}-m_{\mathrm{B}^{*+}}$, with the latter being measured for the first time.