Using data samples with an integrated luminosity of 5.85 fb^{-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^{-}→K^{+}K^{-}J/ψ. A new resonance with a mass of M=4708_{-15}^{+17}±21 MeV/c^{2} and a width of Γ=126_{-23}^{+27}±30 MeV is observed in the energy-dependent line shape of the e^{+}e^{-}→K^{+}K^{-}J/ψ cross section with a significance over 5σ. The K^{+}J/ψ 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^{-}→K^{-}Z_{cs}(3985)^{+}/K^{-}Z_{cs}(4000)^{+}+c.c. with Z_{cs}(3985)^{±}/Z_{cs}(4000)^{±}→K^{±}J/ψ are reported at 90% confidence levels. The ratio of branching fractions {[B(Z_{cs}(3985)^{+}→K^{+}J/ψ)]/B[Z_{cs}(3985)^{+}→(D[over ¯]^{0}D_{s}^{*+}+D[over ¯]^{*0}D_{s}^{+})]} is measured to be less than 0.03 at 90% confidence level.