  Using $e^+e^-$ collision data collected with the BESIII detector at the
BEPCII collider at center-of-mass energies between 3.510 and 4.914GeV,
corresponding to an integrated luminosity of 25 fb$^{-1}$, we measure the Born
cross sections for the process $e^+e^-\to K^-\bar{\Xi}^+\Lambda/\Sigma^{0}$ at
thirty-five energy points with a partial-reconstruction strategy. By fitting
the dressed cross sections of $e^+e^-\to K^-\bar{\Xi}^+\Lambda/\Sigma^{0}$,
evidence for $\psi(4160) \to K^{-}\bar\Xi^{+}\Lambda$ is found for the first
time with a significance of 4.4$\sigma$, including systematic uncertainties. No
evidence for other possible resonances is found. In addition, the products of
electronic partial width and branching fraction for all assumed resonances
decaying into $K^{-}\bar\Xi^{+}\Lambda/\Sigma^{0}$ are determined.
