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The cross section of the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\eta}}^{\ensuremath{'}}J/\ensuremath{\psi}$ is measured at center-of-mass (c.m.) energies from $\sqrt{s}=4.178$ to 4.600 GeV using data samples corresponding to a total integrated luminosity of $11\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ collected with the BESIII detector operating at the BEPCII storage ring. The dependence of the cross section on $\sqrt{s}$ …