A UAV-assisted cellular network can provide ubiquitous links to everything and it is considered to be one of the key technologies for 6G wireless networks. In this paper, we consider an uplink wireless network with a macrobase station (MBS) and cellular users. However, the coverage equality of edge users cannot be guaranteed in scenarios where data service is dense. Specifically, a novel topology of the UAV-assisted wireless network is considered. UAVs are deployed upon the cell edge to serve edge users with poor communication quality. To avoid larger interference caused by users and UAVs in the overlapping area, the locations of these UAVs are modeled as a homogeneous Poisson point process (HPPP) under the Poisson cluster distance constraint (PCDC). In addition, we assume that edge users cluster around each UAV and model their locations as Poisson cluster processes (PCPs). Initially, the Laplace transforms of intra-cluster interference, inter-cluster interference, and other interference are derived. Subsequently, coverage probability and area spectrum efficiency are derived for UAVs and MBS using tools from stochastic geometry. Moreover, the energy efficiency of the system is obtained. Simulation results are examined to validate the accuracy of theoretical analysis and provide insights into the effects of the system parameters as well as useful guidelines for practical system design.