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