  In this work, we investigate the effect of Population~III~(Pop.~III) stars in
ultracompact minihalos~(UCMHs) on the cosmic ionization history using the
Planck observation data. Although high-redshift astrophysics is not understood
yet, UCMHs could host the Pop.~III stars like the halos formed in the standard
structure formation scenario. Such Pop.~III stars would emit ionizing photons
during their main sequence and facilitate cosmic reionization in high
redshifts. To study their effects on the global ionization, we model the cosmic
reionization evolution based on the ``tanh"-type reionization model which is
expressed by $z_{\mathrm{reio}}$ with additional two parameters characterizing
the initial mass of UCMHs and the number density of UCMHs. We implement the
Monte Carlo Markov Chain analysis with the latest Planck observation data for
our reionization model. As the result, we found that if the UCMH initial mass
is larger than $10^{8.4}\mathrm{M}_{\odot}$, the number density of UCMHs is
strictly limited. Then we obtained the constraint on the amplitude of the
primordial power spectrum through the constraint on the UCMH number density
like $\mathcal{A}_{\zeta}\lesssim 10^{-8}$ in the scales, $k\lesssim
50\mathrm{Mpc}^{-1}$, when we assume that the standard ``tanh"-type
reionization occurs by $z=3$, so that we set $z_{\mathrm{reio}}>3$.
