Generation of multi-photon entangled states with high efficiency in integrated photonic quantum systems is still a big challenge. The usual three-photon generation efficiency based on the third-order nonlinear effect is extremely low. Here, we propose a scheme to generate three-photon correlated states, which are entangled states in frequency space and bound states in real space, with high efficiency. This method relies on two crucial processes. On one hand, by employing a Sagnac interferometer, an incident photon can be transformed into a symmetric superposition of the clockwise and counterclockwise modes of the Sagnac loop, which can then be perfectly absorbed by the emitter. On the other hand, the coupling strengths of the two transition paths of the emitter to the Sagnac loop are set to be equal, under which the absorbed photon can be emitted completely from the cascaded transition path due to quantum interference. By adjusting the coupling strengths among the three transition paths of the emitter and the waveguide modes, we can control the spectral entanglement and spatial separation among the three photons. Our proposal can be used to generate three-photon entangled states on demand, and the efficiency can be higher than 90% with some practical parameters, which can find important applications in integrated quantum information processing.