We analysed the gas-phase metallicity properties of a sample of low-stellar-mass (log M_⋆/M_⊙ ≲ 9) galaxies at 3 < z < 10 observed with JWST/NIRSpec as part of the JADES programme in its deep GOODS-S tier. By combining this sample with more massive galaxies at similar redshifts from other programmes, we study the scaling relations between stellar mass (M_⋆), oxygen abundance (O/H), and star-formation rate (SFR) for 146 galaxies spanning three orders of magnitude in stellar mass and out to the epoch of early galaxy assembly. We find evidence for a shallower slope at the low-mass end of the mass–metallicity relation (MZR), with 12+log(O/H) = (7.72 ± 0.02) + (0.17 ± 0.03) log(M_⋆/10⁸ M_⊙), in good agreement with the MZR probed by local analogues of high-redshift systems, such as the ‘Green Pea’ and ‘Blueberry’ galaxies. The inferred slope is well matched by models including ‘momentum-driven’ supernova (SN) winds, suggesting that feedback mechanisms in dwarf galaxies (and at high z) might be different from those in place at higher masses. The evolution in the normalisation is observed to be relatively mild compared to previous determinations of the MZR at z ∼ 3 (∼0.1 − 0.2 dex across the explored mass regime). We observe a deviation from the local fundamental metallicity relation (FMR) for our sample at high redshift, especially at z > 6, with galaxies significantly less enriched than predicted given their M_⋆ and SFR (with a median offset in log(O/H) of ∼0.5 dex, significant at ∼5σ). These observations are consistent with an enhanced stochasticity in the gas accretion and star-formation history of high-redshift systems, prompting us to reconsider the nature of the relationship between M_⋆, O/H, and SFR in the early Universe.