  We investigate the distribution of metals in the cosmological volume at
$z\sim3$, in particular, provided by massive population III (Pop III) stars
using a cosmological $N$-body simulation in which a model of Pop III star
formation is implemented. Owing to the simulation, we can choose minihaloes
where Pop III star formation occurs at $z>10$ and obtain the spatial
distribution of the metals at lower-redshifts. To evaluate the amount of heavy
elements provided by Pop III stars, we consider metal yield of pair-instability
or core-collapse supernovae (SNe) explosions of massive stars. By comparing our
results to the Illustris-1 simulation, we find that heavy elements provided by
Pop III stars often dominate those from galaxies in low density regions. The
median value of the volume averaged metallicity is $Z\sim 10^{-4.5 - -2}
Z_{\odot}$ at the regions. Spectroscopic observations with the next generation
telescopes are expected to detect the metals imprinted on quasar spectra.
