  The Born cross sections are measured for the first time for the processes
$e^+e^-\to D_s^{*+}D_{s0}^*(2317)^- +c.c.$ and $e^+e^-\to
D_s^{*+}D_{s1}(2460)^- +c.c.$ at the center-of-mass energy $\sqrt{s}=$
4.600~GeV, 4.612~GeV, 4.626~GeV, 4.640~GeV, 4.660~GeV, 4.68~GeV, and 4.700~GeV,
and for $e^+e^-\to D_s^{*+}D_{s1}(2536)^- +c.c.$ at $\sqrt{s}=$ 4.660~GeV,
4.680~GeV, and 4.700~GeV, using data samples collected with the BESIII detector
at the BEPCII collider. No structures are observed in cross-section
distributions for any of the processes.
