  Stellar and supernova nucleosynthesis in the first few billion years of the
cosmic history have set the scene for early structure formation in the
Universe, while little is known about their nature. Making use of stellar
physical parameters measured by GALAH Data Release 3 with accurate astrometry
from the Gaia EDR3, we have selected $\sim 100$ old main-sequence turn-off
stars (ages $\gtrsim 12$ Gyrs) with kinematics compatible with the Milky Way
stellar halo population in the Solar neighborhood. Detailed homogeneous
elemental abundance estimates by GALAH DR3 are compared with supernova yield
models of Pop~III (zero-metal) core-collapse supernovae (CCSNe), normal
(non-zero-metal) CCSNe, and Type Ia supernovae (SN Ia) to examine which of the
individual yields or their combinations best reproduce the observed elemental
abundance patterns for each of the old halo stars ("OHS"). We find that the
observed abundances in the OHS with [Fe/H]$>-1.5$ are best explained by
contributions from both CCSNe and SN~Ia, where the fraction of SN~Ia among all
the metal-enriching SNe is up to 10-20 % for stars with high [Mg/Fe] ratios and
up to 20-27 % for stars with low [Mg/Fe] ratios, depending on the assumption
about the relative fraction of near-Chandrasekhar-mass SNe Ia progenitors. The
results suggest that, in the progenitor systems of the OHS with [Fe/H]$>-1.5$,
$\sim$ 50-60% of Fe mass originated from normal CCSNe at the earliest phases of
the Milky Way formation. These results provide an insight into the birth
environments of the oldest stars in the Galactic halo.
