  We perform weak lensing tomographic peak studies using the first-year shear
data from Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) survey. The
effective area used in our analyses after field selection, mask and boundary
exclusions is $\sim 58 \deg^2$. The source galaxies are divided into low- and
high-redshift bins with $0.2\le z_p\le0.85$ and $0.85\le z_p\le1.5$,
respectively. We utilize our halo-based theoretical peak model including the
projection effect of large-scale structures to derive cosmological constraints
from the observed tomographic high peak abundances with the signal-to-noise
ratio in the range of $\nu_{\rm N}=[3.5,5.5]$. These high peaks are closely
associated with the lensing effects of massive clusters of galaxies. Thus the
inclusion of their member galaxies in the shear catalog can lead to significant
source clustering and dilute their lensing signals. We account for this
systematic effect in our theoretical modelling. Additionally, the impacts of
baryonic effects, galaxy intrinsic alignments, as well as residual
uncertainties in shear and photometric redshift calibrations are also analyzed.
Within the flat $\Lambda$CDM model, the derived constraint is
$S_8=0.758_{-0.076}^{+0.033}$ and $0.768_{-0.057}^{+0.030}$ with the source
clustering information measured from the two cluster catalogs, CAMIRA and WZL,
respectively. The asymmetric uncertainties are due to the different degeneracy
direction of $(\Omega_{\rm m}, \sigma_8)$ from high peak abundances comparing
to that from the cosmic shear two-point correlations which give rise
approximately the power index $\alpha=0.5$. Fitting to our constraints, we
obtain $\alpha\approx 0.38$ and $\Sigma_8=0.772_{-0.032}^{+0.028}$ (CAMIRA) and
$0.781_{-0.033}^{+0.028}$ (WZL). In comparison with the results from
non-tomographic peak analyses, the $1\sigma$ uncertainties on $\Sigma_8$ are
reduced by a factor of $\sim1.3$.
