### Abstract:

We report in detail on searches for eV-scale sterile neutrinos, in the context of a \(3+1\) model, using eight years of data from the IceCube Neutrino Telescope. By analyzing the reconstructed energies and zenith angles of 305,735 atmospheric \({\nu }_{\mu }\) and \({\overline{\nu }}_{\mu }\) events we construct confidence intervals in two analysis spaces: \({\mathrm{sin}}^{2}\left(2{\theta }_{24}\right)\) vs \(\Delta {m}_{41}^{2}\) under the conservative assumption \({\theta }_{34}=0\); and \({\mathrm{sin}}^{2}\left(2{\theta }_{24}\right)\) vs \({\mathrm{sin}}^{2}\left(2{\theta }_{34}\right)\) given sufficiently large \(\Delta {m}_{41}^{2}\) that fast oscillation features are unresolvable. Detailed discussions of the event selection, systematic uncertainties, and fitting procedures are presented. No strong evidence for sterile neutrinos is found, and the best-fit likelihood is consistent with the no sterile neutrino hypothesis with a \(p\) value of 8% in the first analysis space and 19% in the second.