  Using data samples collected by the BESIII detector operating at the BEPCII
storage ring, we measure the $e^+e^- \to K_{S}^{0}K^{\pm}\pi^{\mp}$ Born cross
sections at center-of-mass energies between 3.8 and 4.6\,GeV, corresponding to
a luminosity of about 5.0~fb$^{-1}$. The results are compatible with the BABAR
measurements, but with the precision significantly improved. A simple $1/s^n$
dependence for the continuum process can describe the measured cross sections,
but a better fit is obtained by an additional resonance near 4.2\,GeV, which
could be an excited charmonium or a charmonium-like state.
