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The processes 𝑒+𝑒−→𝐷+ 𝑠𝐷𝑠1(2460)−+c.c. and 𝑒+𝑒−→𝐷*+ 𝑠𝐷𝑠1(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−→𝐷+ 𝑠𝐷𝑠1(2460)−+c.c. at nine center-of-mass energies between 4.467 GeV and 4.600 GeV and those of 𝑒+𝑒−→𝐷*+ 𝑠𝐷𝑠1(2460)−+c.c. at √𝑠=4.590 GeV and 4.600 GeV are measured. No obvious charmonium or charmoniumlike structure is seen in the measured cross sections.