2025ApJ...986L..24J

The gravitational potential is established as a critical determinant of gas-phase metallicity (12+log(O/H)) in low-redshift galaxies, whereas its influence remains unconfirmed at high redshifts. We investigate the correlation between gas-phase metallicity and effective radius (R_e) for a sample of galaxies with redshifts ranging from 1 to 7, drawn from JWST Advanced Deep Extragalactic Survey Data Release 3. We calculate the metallicities using four strong-line methods: N2S2Hα, R23, N2, and O3N2. After taking out the evolution of size, we find that the offsets of the mass-size relation (${\rm{\Delta }}\mathrm{log}{R}_{{\rm{e}}}$) are significantly negatively correlated with the offset of the mass-metallicity relation (${\rm{\Delta }}\mathrm{log}({\rm{O}}/{\rm{H}})$) for the four metallicity tracers. Regardless of the metallicity tracer used, we obtain Spearman rank p-values much less than 0.01, rejecting the null hypothesis that the observed correlation is statistically nonsignificant and attributable to random chance. This is also true for galaxies with z > 3, with p-values less than 0.05 for the four metallicity tracers. We for the first time find evidence of size playing a key role in determining gas-phase metallicity toward cosmic dawn, suggesting that the gravitational potential influences galaxies' material-exchange processes with the surrounding environment in the very early Universe.