An open quantum system operated at the spectral singularities where dimensionality reduces, known as exceptional points (EPs), demonstrates distinguishing behavior from the Hermitian counterpart. Based on the recently proposed microcavity with exceptional surface (ES), we report and explain the peculiar quantum dynamics in atom-photon interaction associated with EPs: cavity transparency, decoherence suppression beyond the limitation of Jaynes-Cummings (JC) system, and the population trapping of lossy cavity. An analytical description of the local density of states (LDOS) for ES microcavity is derived from an equivalent cavity quantum electrodynamics (QED) model, which goes beyond the single-excitation approximation and allows exploring the quantum effects of EPs on multiphoton process by parametrizing the extended cascaded quantum master equation. It reveals that a square Lorentzian term in LDOS induced by second-order EPs interferes with the linear Lorentzian profile, giving rise to cavity transparency for atom with special transition frequency in the weak coupling regime. This additional contribution from EPs also breaks the limit on dissipation rate of JC system bounded by bare components, resulting in the decoherence suppression with anomalously small decay rate of the long-time dynamics and the Rabi oscillation. Remarkably, we find that the cavity population can be partially trapped at EPs, achieved by forming a bound dressed state in the limiting case of vanishing atom decay. Our work unveils the exotic phenomena unique to EPs in cavity QED systems, which opens the door for controlling light-matter interaction at the quantum level through non-Hermiticity, and holds great potential in building high-performance quantum-optics devices.