Performing positioning of future mobile devices using trilateration through radio access networks would provide a robust alternative to currently used global navigation satellite systems. However, the positioning accuracy is strongly dependent on the time synchronization accuracy of the antennas used as location reference points. Consequently, achieving sub-30 cm positioning accuracies requires the synchronization of radio access network antennas to sub-nanosecond accuracy. Here we show a clock phase synchronization and optical clock signal distribution approach to clock synchronization in radio access networks that achieves 0.98-ps root-mean-square precision clock synchronization, in a real-time field-trial demonstration on 37.6-km dark fiber, with optical clock frequency synchronization and clock phase caching operating using 25.6-Gb/s commercial transceivers. We quantify the clock synchronization performance of our approach using standard metrics, including time deviation (TDEV) and mean time interval error (MTIE). Furthermore, we estimate the impact of varying the phase update rate used in clock phase caching on the clock synchronization performance of our approach. Through our two combined approaches, we explore a route towards achieving sub-nanosecond clock synchronization in radio access networks.