Abstract: With the development of millimeter-wave (mmWave) communication systems, large-scale reconfigurable intelligent surfaces (RISs) have gained considerable attention as a promising technology for signal strength enhancement and coverage extension. However, as the antenna scale and bandwidth increase, RIS-assisted wideband orthogonal frequency division multiplexing (OFDM) communication systems face challenges due to the near-field range expansion and the beam split effect over the high-frequency band, complicating the acquisition of channel state information (CSI). To tackle these challenges, in this paper, we present a codebook-based three-stage beam training scheme by utilizing the beam split effect to bypass CSI estimation. Specifically, by analyzing the beam split effect in RIS-assisted OFDM communication systems, we propose a beam-split-aware codebook capable of covering both the near and far fields with fewer codewords compared to conventional narrow-band codebooks. Using such a codebook, a three-stage beam training mechanism is performed to obtain the optimal codeword with low time overhead, thereby facilitating subsequent beamforming. Simulation results demonstrate that the proposed scheme outperforms existing near- and far-field codebook-based schemes in terms of the beam training resolution and sum rate in the hybrid near-far field.