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Non-Hermitian spectral degeneracies, known as exceptional points (EPs), feature simultaneous coalescence of both eigenvalues and the associated eigenstates of a system. A host of intriguing EP effects and their applications have been revealed in the classical realm, such as loss-induced lasing, single-mode laser, and EP-enhanced sensing. Here we show that a purely quantum effect, known as single-photon blockade, emerges in a Kerr microring resonator due to EP-induced asymmetric coupling between the optical modes and the nonlinearity-induced anharmonic energy-level spacing. A striking feature of this photon blockade is that it emerges at two-photon resonance which in Hermitian systems will only lead to photon-induced tunneling but not to photon blockade. By tuning the system towards to or away from an EP, one can control quantum correlations, implying the potential use of our system for frequency tunable single-photon generation and an antibunching-to-bunching light switch. Our work sheds new light on EP-engineered purely quantum effects, providing unique opportunities for making and utilizing various single-photon quantum EP devices.