  We systematically investigated the heating of coronal loops on metal-free
stars with various stellar masses and magnetic fields by magnetohydrodynamic
simulations. It is found that the coronal property is dependent on the coronal
magnetic field strength $B_{\rm c}$ because it affects the difference of the
nonlinearity of the Alfv\'{e}nic waves. Weaker $B_{\rm c}$ leads to cooler and
less dense coronae because most of the input waves dissipate in the lower
atmosphere on account of the larger nonlinearity. Accordingly EUV and X-ray
luminosities also correlate with $B_{\rm c}$, while they are emitted in a wide
range of the field strength. Finally we extend our results to evaluating the
contribution from low-mass Population III coronae to the cosmic reionization.
Within the limited range of our parameters on magnetic fields and loop lengths,
the EUV and X-ray radiations give a weak impact on the ionization and heating
of the gas at high redshifts. However, there still remains a possibility of the
contribution to the reionization from energetic flares involving long magnetic
loops.
