Measurement of the Born cross sections for ${e}^{+}{e}^{-}\to {D}_{s}^{+}{D}_{s1}\left(2460{\right)}^{-}+c.c.$ and ${e}^{+}{e}^{-}\to {D}_{s}^{*+}{D}_{s1}\left(2460{\right)}^{-}+c.c.$

The processes ${e}^{+}{e}^{-}\to {D}_{s}^{+}{D}_{s1}\left(2460{\right)}^{-}+c.c.$ and ${e}^{+}{e}^{-}\to {D}_{s}^{*+}{D}_{s1}\left(2460{\right)}^{-}+c.c.$ are studied for the first time using data samples collected with the BESIII detector at the BEPCII collider. The Born cross sections of ${e}^{+}{e}^{-}\to {D}_{s}^{+}{D}_{s1}\left(2460{\right)}^{-}+c.c.$ at nine center-of-mass energies between 4.467 GeV and 4.600 GeV and those of ${e}^{+}{e}^{-}\to {D}_{s}^{*+}{D}_{s1}\left(2460{\right)}^{-}+c.c.$ at $\sqrt{s}=4.590\text{}\text{}\mathrm{GeV}$ and 4.600 GeV are measured. No obvious charmonium or charmoniumlike structure is seen in the measured cross sections.