Study of $e^{+}{e}^{-}\to \gamma \phi J\mathrm{/}\psi$ from $\sqrt{s}=4.600$ to $4.951$ GeV

Using data samples with an integrated luminosity of $6.4$~fb${}^{-1}$ collected by the BESIII detector operating at the BEPCII storage ring, the process of $e^{+}{e}^{-}\to \gamma \phi J\mathrm{/}\psi$ is studied. The processes of $e^{+}{e}^{-}\to \phi {\chi }_{c1,c2}$, ${\chi }_{c1,c2}\to \gamma J\mathrm{/}\psi$ are observed with a significance of more than $10\sigma$. The $\sqrt{s}$-dependent cross section of $e^{+}{e}^{-}\to \phi {\chi }_{c1,c2}$ is measured between 4.600 and 4.951~GeV, and evidence of a resonance structure is found for the first time in the $\phi {\chi }_{c2}$ process. We also search for the processes of $e^{+}{e}^{-}\to \gamma X(4140)$, $\gamma X(4274)$ and $\gamma X(4500)$ via the $\gamma \phi J\mathrm{/}\psi$ final state, but no obvious structures are found. The upper limits on the production cross section times the branching fraction for these processes at the 90% confidence level are reported.