In the field of clock synchronization, the application of frequency-entangled source is a promising direction to improve accuracy and security. In this paper, we analyze the performance of the twin-beam state and the difference-beam state using a practical second-order interference-based scheme. The advantages of the twin-beam state are pointed out especially for the dispersion-free property of HOM interference in a long-distance clock transfer. With the introduction of dispersion-compensated material, our experimental system based on a twin-beam state achieves a clock accuracy at 4 ps with a time offset precision of 1.8 ps over 10 s acquisition time while the time deviation is 0.15 ps over an averaging time of 5500 s in a 22 km-long transmission. These properties exhibit a leading position compared with the current clock synchronization system using the same theoretical scheme and also competitive among the implementations using other second-order interference-based schemes.