JADES: Carbon-enhanced, Nitrogen-normal compact galaxy at z=11.2

Over the past few years \textit{JWST} has been a major workhorse in detecting and constraining the metal enrichment of the first galaxies in the early Universe and finding the source of the ionisation of their interstellar medium. In this work, we present new deep JWST/NIRSpec spectroscopy of GS-z11-1, a galaxy at z = 11.28, in which we report the detection of multiple rest-frame UV and optical emission lines: CIII]$λλ$1907,09, CIV]$λλ$1548,51, [OII]$λλ$3726,29, [NeIII]$λ$3869, H$γ$ and tentative evidence for HeII$λ$1640. The ionisation properties of GS-z11-1 are consistent with star formation, with potential contribution from an active galactic nucleus (AGN). We estimate a galaxy stellar mass of log(M$_{*}$/M$_{\odot}$) = 7.8$\pm$0.2 and log(SFR/(M$_{\odot}$ yr$^{-1}$))= 0.32$\pm$0.11 for the fiducial SF-only models. We measured C/O from the SED modelling of C/O = 1.20$\pm0.15 \times$ solar. This is one of the highest C/O abundances at z$>$10, and it is consistent with either PopII and PopIII enrichment paths. Despite this source being extremely compact, with a half-light radius of 73$\pm$10 pc, we see no increased equivalent width of NIV] and NIII] emission lines as seen in some other compact sources at similar redshifts, a potential signature of second-generation stars in GCs. Overall, this galaxy exhibits low metallicity and high ionisation parameter consistent with intense star-formation or AGN activity in the early Universe, possibly observed before the enrichment by the second generation of stars in proto-globular clusters in the core of the galaxy.