(Abridged) JWST has revealed extremely compact stellar clumps in galaxies at z>6, but their formation mechanism and subsequent evolution remain uncertain. We investigate whether such systems can form in-situ through the fragmentation of an early galactic disk and how stellar feedback regulates their properties. We perform a suite of radiation-hydrodynamical simulations of an isolated galaxy ("Ninfea_blu"), with rm Mᵥᵢᵣ=1.5×10¹⁰ M_⊙, evolved for 100 Myr from z=16 to 12.5 with a maximum spatial resolution of 3.6 pc. In all cases, the gas rapidly forms a rotationally supported disk, reaches a peak star formation rate of 10-15rm M_⊙ yr⁻¹, and fragments into dense stellar clumps. Toomre-unstable regions (Q_(rm gas)<1) appear before the onset of star formation, and the first stellar structures form preferentially within these regions, supporting a Toomre-like gravitational fragmentation pathway.The clumps have stellar masses of 10⁶-2×10⁸ M_⊙, effective radii of 7-50 pc, and surface densities of 0.2-3×10⁴rm M_⊙ pc⁻², overlapping much of the parameter space occupied by observed z>6 clumps. Feedback reduces the cumulative stellar mass by 30-40%, lowers the gas mass retained within clumps by ~1 dex, and suppresses their high-mass tail without preventing their initial formation. Clumps subsequently migrate, interact, undergo tidal stripping, and disperse. The clump mass function produces a power law slope of -1.88, which aligns closely with observations. Moreover, their contributions to the stellar mass and intrinsic UV luminosity decline from 0.41 and 0.40 at 20 Myr to 0.13 and 0.10 at 100 Myr, respectively. We conclude that fragmentation of compact, gas-rich disks provides a viable origin for many of the dense stellar systems observed in the early Universe, while feedback and internal dynamics primarily regulate their growth and fate.