Precise time synchronization is a fundamental challenge in distributed quantum systems, with direct implications for secure communication, quantum sensing, and next-generation quantum network technologies. In this work, we present an field programmable gate arrays (FPGA)-based implementation of a synchronization system using time-correlated entangled photons (TCEP), achieving timing precision below 200 ps across 10- and 20-km deployed fiber links using spectral filtering (SF) and dispersion compensation. The system exploits the intrinsic temporal correlations of entangled photon pairs to estimate synchronization offsets between remote nodes. A modular architecture is developed, featuring optimized OpenCL kernels for real-time correlation, timestamp aggregation, and peak normalization. This enables high-throughput performance with efficient utilization of hardware resources. Experimental validation confirms that the FPGA processes entangled photon timestamps and computes cross-correlation functions significantly faster than conventional CPU-based methods, achieving execution times in the range of a few milliseconds for datasets containing up to 105 timestamped events per node. Resource utilization analysis further demonstrates the scalability of the design, with the system operating reliably at a 397.5-MHz clock frequency while maintaining efficient logic, register, and memory usage. Our results illustrate the feasibility of deploying FPGA-based TCEP synchronization in real-world quantum networks, supporting applications in ultra-reliable low-latency communication, distributed quantum computing, and quantum-enhanced localization and sensing. This work bridges foundational quantum photonic principles and hardware-level deployment, laying the groundwork for timing infrastructure in future quantum internet and 6G networks.