Most systems used in quantum physics experiments require the efficient and simultaneous recording different multi-photon coincidence detection events. In such experiments, the single-photon gated counting systems can be applicable. The main sources of errors in these systems are both instability of the clock source and their imperfect synchronization with the excitation source. Below, we propose a solution for improvement of the metrological parameters of such measuring systems. Thus, we designed a novel integrated circuit dedicated to registration of signals from a photon number resolving detectors including a phase synchronizer module. This paper presents the architecture of a high-resolution (~60 ps) digital phase synchronizer module cooperating with a multi-channel coincidence counter. The main characteristic feature of the presented system is its ability to fast synchronization (requiring only one clock period) with the measuring process. Therefore, it is designed to work with various excitation sources of a very wide frequency range. Implementation of the phase synchronizer module in an FPGA device enabled to reduce the synchronization error value from 2.857 ns to 214.8 ps.