According to the leading cosmological model, a first generation of stars called Population III (PopIII), condensed almost entirely out of hydrogen and helium, must have initiated the creation of all heavier chemical elements. Here we report the detection of ionised hydrogen (H$γ_{4342}$) with $S/N$=5.9 in a region about 3 pkpc (projected) North-East from the z~10.6 galaxy GN-z11, where line emission compatible with doubly ionised helium (HeII$_{1640}$) had been found. Our new JWST/NIRSpec-IFS G395H data confirm the authenticity of the previous detection, at a redshift of $z_{\rm Hγ}$=$10.5862$$\pm$$0.0003$. H$δ$ is marginally detected ($S/N$$\sim$$2$). No metal lines are detected in our observations spanning $λ_{\rm rest}$=$0.25$-$0.45μ$m. We derive a $3σ$ upper limit on the gas phase metallicity of 12+log(O/H)$<$6.96 ($Z_{\rm gas}$$<$$0.019~Z_\odot$). Through comparison with NIRCam imaging, we constrain a lower limit on the equivalent width of EW$_0$(H$γ$)$>$350Å. We compare our emission line constraints to model predictions and find them compatible with photoionization by PopIII stars, possibly intermixed with next-generation (PopII) stars. We infer an upper limit on the dynamical mass of $M_{\rm dyn}$$\lesssim$$3$$\times$$10^8M_\odot$. Our data provide novel support for the presence of PopIII stars nearby GN-z11, 440 Myr after the Big Bang.