Sterile neutrinos with $\sim 1$ eV mass scale can resolve anomalies reported in short-baseline neutrino oscillation experiments. The same sterile neutrinos can affect the atmospheric neutrino fluxes at the detectors such as IceCube in the TeV energy range. Recent IceCube search results for a sterile neutrino resulted in stringent constraints on its mass and mixing with active neutrinos, essentially excluding the parameter space favored by the short-baseline experiments. In our recent reanalysis of IceCube data we show that sterile-active neutrino mixing schemes affect interpretation of the excluded parameter regions. We present exclusion regions in the mixing angle range $0.01 \le \sin^2\theta_{24} \le 0.1$ and mass-squared difference range $0.1~{\rm eV}^2 \le \Delta m_{42}^2 \le 10~{\rm eV}^2$ for the mass-mixing and flavor-mixing schemes. We exclude the parameter space favored by recent MiniBooNE analysis at $\gtrsim 2\sigma$~CL for both schemes. Furthermore, we find that a prompt atmospheric neutrino flux contribution can relax the constraints on the sterile neutrino mass-squared difference for $\Delta m_{42}^2 \gtrsim 1~{\rm eV}^2$.