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.
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