  We introduce a new set of zoom-in cosmological simulations with sub-pc
resolution, intended to model extremely faint, highly magnified star-forming
stellar clumps, detected at z=6.14 thanks to gravitational lensing. The
simulations include feedback from individual massive stars (in both the
pre-supernova and supernova phases), generated via stochastic, direct sampling
of the stellar initial mass function. We adopt a modified 'delayed cooling'
feedback scheme, specifically created to prevent artificial radiative loss of
the energy injected by individual stars in very dense gas (n~10^3-10^5
cm^{-3}). The sites where star formation ignites are characterised by maximum
densities of the order of 10^5 cm^{-3} and gravitational pressures P/k>10^7
K/cm^3, corresponding to the values of the local, turbulent regions where the
densest stellar aggregates form. The total stellar mass at z=6.14 is 3.4x10^7
M_sun, in satisfactory agreement with the observed stellar mass of the observed
systems. The most massive clumps have masses of ~10^6 M_sun and half-mass sizes
of ~100 pc. These sizes are larger than the observed ones, including also other
samples of lensed high-redshift clumps, and imply an average density one order
of magnitude lower than the observed one. In the size-mass plane, our clumps
populate a sequence that is intermediate between the ones of observed
high-redshift clumps and local dSph galaxies.
