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5th Generation Mobile Communication Technology (5G) utilizes the Access Traffic Steering, Switching, and Splitting (ATSSS) rule to enable multi-path data transmission, which is currently being standardized. Recently, the 3rd Generation Partnership Project (3GPP) SA1 and SA2 have been working on the multi-path solution for possible improvement from different perspectives. However, the existing 3GPP multi-path solution has some limitations on ultra-reliable low-latency communication (URLLC) traffic in terms of reliability and latency requirements. In order to capture the potential gains of multi-path architecture in the context of URLLC services, this paper proposes a novel traffic splitting technique that can more efficiently enjoy the benefit of multi-path architecture in reducing user equipment (UE) uplink (UL) end-to-end (E2E) latency. In particular, we formulate an optimization framework that minimizes user's UL E2E latency via the joint optimization on the ratio of traffic assigned to each path and their corresponding transmit power. The performance of the proposed scheme is evaluated via well-designed simulations.