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The e+e−→D+sDs1(2536)− and e+e−→D+sD∗s2(2573)− processes are studied using data samples collected with the BESIII detector at center-of-mass energies from 4.530 to 4.946~GeV. The absolute branching fractions of Ds1(2536)−→D¯∗0K− and D∗s2(2573)−→D¯0K− are measured for the first time to be (35.9±4.8±3.5)% and (37.4±3.1±4.6)%, respectively. The measurements are in tension with predictions based on the assumption that the Ds1(2536) and D∗s2(2573) are dominated by a bare cs¯ component. The e+e−→D+sDs1(2536)− and e+e−→D+sD∗s2(2573)− cross sections are measured, and a resonant structure at around 4.6~GeV with a width of 50~MeV is observed for the first time with a statistical significance of 15σ in the e+e−→D+sD∗s2(2573)− process. It could be the Y(4626) found by the Belle collaboration in the D+sDs1(2536)− final state, since they have similar masses and widths. There is also evidence for a structure at around 4.75~GeV in both processes.