Search for $X\left(1870\right)$ via the decay $J/\psi \to \omega K^{+}{K}^{-}\eta$

Using a sample of $(10087\pm 44)\times {10}^{6}J/\psi$ events collected by the BESIII detector at the BEPCII collider, we search for the decay $X\left(1870\right)\to K^{+}{K}^{-}\eta$ via the $J/\psi \to \omega K^{+}{K}^{-}\eta$ process for the first time. No significant $X\left(1870\right)$ signal is observed. The upper limit on the branching fraction of the decay $J/\psi \to \omega X\left(1870\right)\to \omega K^{+}{K}^{-}\eta$ is determined to be $9.55\times {10}^{-7}$ at the 90% confidence level. In addition, the branching faction $B(J/\psi \to \omega K^{+}{K}^{-}\eta )$ is measured to be $(3.33\pm 0.02(\mathrm{stat})\pm 0.12(\mathrm{syst}\left)\right)\times {10}^{-4}$.