The e^{+}e^{-}→D_{s}^{+}D_{s1}(2536)^{-} and e^{+}e^{-}→D_{s}^{+}D_{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 D_{s1}(2536)^{-}→D[over ¯]^{*0}K^{-} and D_{s2}^{*}(2573)^{-}→D[over ¯]^{0}K^{-} are measured for the first time to be (35.9±4.8±3.5)% and (37.4±3.1±4.6)%, respectively. The e^{+}e^{-}→D_{s}^{+}D_{s1}(2536)^{-} and e^{+}e^{-}→D_{s}^{+}D_{s2}^{*}(2573)^{-} cross sections are measured, and a resonant structure at around 4.6 GeV with a width of 50 MeV is observed in both processes with a statistical significance of 7.2σ and 15σ, respectively. The state is observed for the first time in e^{+}e^{-}→D_{s}^{+}D_{s2}^{*}(2573)^{-} and could be the Y(4626) found by the Belle oration in the D_{s}^{+}D_{s1}(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.