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Using data samples with an integrated luminosity of 5.85~fb$^{-1}$ collectedat center-of-mass energies from 4.61 to 4.95 GeV with the BESIII detectoroperating at the BEPCII storage ring, we measure the cross section for theprocess $e^+e^-\to K^+K^-J/\psi$. A new resonance with a mass of $M =4708_{-15}^{+17}\pm21$ MeV/$c^{2}$ and a width of $\Gamma =126_{-23}^{+27}\pm30$ MeV is observed in the energy-dependent line shape of the$e^+e^-\to K^+K^-J/\psi$ cross section with a significance over $5\sigma$. The$K^{+}J/\psi$ system is also investigated to search for charged charmoniumlikestates, but no significant $Z_{cs}^+$ states are observed. Upper limits on theBorn cross sections for $e^+e^-\to K^{-} Z_{cs}(3985)^{+}/K^{-}Z_{cs}(4000)^{+} + c.c.$ with $Z_{cs}(3985)^{\pm}/Z_{cs}(4000)^{\pm}\to K^{\pm}J/\psi$ are reported at 90\% confidence levels. The ratio of branchingfractions $\frac{\mathcal{B}(Z_{cs}(3985)^{+}\to K^+J/\psi)}{\mathcal{B}(Z_{cs}(3985)^{+}\to (\bar{D}^{0}D_s^{*+} +\bar{D}^{*0}D_s^+))}$ is measured to be less than 0.03 at 90\% confidencelevel.

Observation of a vector charmoniumlike state at 4.7 ${\rm GeV}/c^2$ and search for $Z_{cs}$ in $e^+e^-\to K^+K^-J/\psi$