The International Linear Collider (ILC) will allow the precise study of $$e^{-}e^{+} \rightarrow q\bar{q}$$ $e^{-}{e}^{+}\to q\overline{q}$ interactions at different center-of-mass energies from the $$Z$$ $Z$ -pole to 1 TeV. In this paper, we discuss the experimental prospects for measuring differential observables in $$e^{-}e^{+} \rightarrow b\bar{b}$$ $e^{-}{e}^{+}\to b\overline{b}$ and $$e^{-}e^{+} \rightarrow c\bar{c}$$ $e^{-}{e}^{+}\to c\overline{c}$ at the ILC baseline energies, 250 and 500 GeV. The study is based on full simulation and reconstruction of the International Large Detector (ILD) concept. Two gauge-Higgs unification models predicting new high-mass resonances beyond the Standard Model are discussed. These models predict sizable deviations of the forward–backward observables at the ILC running above the Z mass and with longitudinally polarized electron and positron beams. The ability of the ILC to probe these models via high-precision measurements of the forward–backward asymmetry is discussed. Alternative scenarios at other energies and beam polarization schemes are also discussed, extrapolating the estimated uncertainties from the two baseline scenarios.