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The existence of a quiescent core (QC) in the center of turbulent channel flows was demonstrated in recent experimental and numerical studies. The QC-region, which is characterized by relatively uniform velocity magnitude and weak turbulence levels, occupies about $40\%$ of the cross-section at Reynolds numbers $Re_τ$ ranging from $1000$ to $4000$. The influence of the QC region and its boundaries on transport and accumulation of inertial particles has never been investigated before. Here, we first demonstrate that a QC is unidentifiable at $Re_τ= 180$, before an in-depth exploration of particle-laden turbulent channel flow at $Re_τ= 600$ is performed. The inertial spheres exhibited a tendency to accumulate preferentially in high-speed regions within the QC, i.e. contrary to the well-known concentration in low-speed streaks in the near-wall region. The particle wall-normal distribution, quantified by means of Voronoï volumes and particle number concentrations, varied abruptly across the QC-boundary and vortical flow structures appeared as void areas due to the centrifugal mechanism. The QC-boundary, characterized by a localized strong shear layer, appeared as a \emph{barrier}, across which transport of inertial particles is hindered. Nevertheless, the statistics conditioned in QC-frame show that the mean velocity of particles outside of the QC was towards the core, whereas particles within the QC tended to migrate towards the wall. Such upward and downward particle motions are driven by similar motions of fluid parcels. The present results show that the QC exerts a substantial influence on transport and accumulation of inertial particles, which is of practical relevance in high-Reynolds number channel flow.