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Using data samples with an integrated luminosity of $5.85\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ collected at center-of-mass energies from 4.61 to 4.95 GeV with the BESIII detector operating at the BEPCII storage ring, we measure the cross section for the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}J/\ensuremath{\psi}$. A new resonance with a mass of $M=470{8}_{\ensuremath{-}15}^{+17}\ifmmode\pm\else\textpm\fi{}21\text{ }\text{ }\mathrm{MeV}/{c}^{2}$ and a width of $\mathrm{\ensuremath{\Gamma}}=12{6}_{\ensuremath{-}23}^{+27}\ifmmode\pm\else\textpm\fi{}30\text{ }\text{ }\mathrm{MeV}$ is observed in the energy-dependent line shape of the ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}J/\ensuremath{\psi}$ cross section with a significance over $5\ensuremath{\sigma}$. The ${K}^{+}J/\ensuremath{\psi}$ system is also investigated to search for charged charmoniumlike states, but no significant ${Z}_{cs}^{+}$ states are observed. Upper limits on the Born cross sections for ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{Z}_{cs}(3985{)}^{+}/{K}^{\ensuremath{-}}{Z}_{cs}(4000{)}^{+}+c.c.$ with ${Z}_{cs}(3985{)}^{\ifmmode\pm\else\textpm\fi{}}/{Z}_{cs}(4000{)}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{K}^{\ifmmode\pm\else\textpm\fi{}}J/\ensuremath{\psi}$ are reported at 90% confidence levels. The ratio of branching fractions ${[\mathcal{B}({Z}_{cs}(3985{)}^{+}\ensuremath{\rightarrow}{K}^{+}J/\ensuremath{\psi})]/\mathcal{B}[{Z}_{cs}(3985{)}^{+}\ensuremath{\rightarrow}({\overline{D}}^{0}{D}_{s}^{*+}+{\overline{D}}^{*0}{D}_{s}^{+})]}$ is measured to be less than 0.03 at 90% confidence level.