  We present posterior sample redshift distributions for the Hyper Suprime-Cam
Subaru Strategic Program Weak Lensing three-year (HSC Y3) analysis. Using the
galaxies' photometry and spatial cross-correlations, we conduct a combined
Bayesian Hierarchical Inference of the sample redshift distributions. The
spatial cross-correlations are derived using a subsample of Luminous Red
Galaxies (LRGs) with accurate redshift information available up to a
photometric redshift of $z < 1.2$. We derive the photometry-based constraints
using a combination of two empirical techniques calibrated on spectroscopic-
and multiband photometric data that covers a spatial subset of the shear
catalog. The limited spatial coverage induces a cosmic variance error budget
that we include in the inference. Our cross-correlation analysis models the
photometric redshift error of the LRGs to correct for systematic biases and
statistical uncertainties. We demonstrate consistency between the sample
redshift distributions derived using the spatial cross-correlations, the
photometry, and the posterior of the combined analysis. Based on this
assessment, we recommend conservative priors for sample redshift distributions
of tomographic bins used in the three-year cosmological Weak Lensing analyses.
