  This Letter presents the result of a 3+1 sterile neutrino search using 10.7
years of IceCube data. We analyze atmospheric muon neutrinos that traverse the
Earth with energies ranging from 0.5 to 100 TeV, incorporating significant
improvements in modeling neutrino flux and detector response compared to
earlier studies. Notably, for the first time, we categorize data into starting
and through-going events, distinguishing neutrino interactions with vertices
inside or outside the instrumented volume, to improve energy resolution. The
best-fit point for a 3+1 model is found to be at $\sin^2(2\theta_{24}) = 0.16$
and $\Delta m^{2}_{41} = 3.5$ eV$^2$, which agrees with previous iterations of
this study. The result is consistent with the null hypothesis of no sterile
neutrinos with a p-value of 3.1\%.
