To have vehicles that are outside the signal coverage of the small cell to be able to offload their data’s receiving from the macro cell to the small cell, this work proposes a method, which is based on the maximum flow concept using the Depth-First Search (DFS) exploring approach, to find multiple feasible \(k\) -hop-limited C-V2X data offloading paths for each data receiving vehicle with the help of sidelink relays. In this work, the Multi-access Edge Computing (MEC) architecture that has the centralized computing capability is adopted to identify whether some qualified \(k\) -hop-limited C-V2X data offloading paths from the small cell to each data receiving vehicle can be found or not. If no path from the small cell to a data receiving vehicle can be found, the corresponding vehicle still receives data from the macro cell. The simulation results demonstrate that the proposed method has the better throughput, the higher data offloading fraction, the lower data loss rate and the lower data transmission time than other small cell data offloading methods.