The Open-Radio Access Network (O-RAN) alliance is leading the evolution of telecommunications towards a greater intelligence, openness, virtualization, and interoperability within mobile networks. The O-RAN standard incorporates of many components the Open-Central Unit (O-CU) and Open-Distributed Unit (O-DU), network slicing and heterogeneous base stations (BS). Together, these innovations have given rise to a three-tiered user association (UA) relationship in a type of network called heterogeneous network (HetNet) with network slicing-enabled. There is an absence of efficient UA schemes for achieving fair resource allocation in such network scenario. Hence, this study formulates the fairness-aware UA problem as a utility-based combinatorial optimization problem, which is computationally hard to solve. Hence, an efficient Binary Particle Swarm Optimization (BPSO)-based UA scheme is proposed to solve the problem. Through simulations of an O-RAN based HetNet with network slicing-enabled, performance of the proposed BPSO-UA scheme is compared against two other baseline UA schemes. Results demonstrate the effectiveness of the proposed BPSO-UA scheme in achieving high fairness through equitable network slicing resource allocation, thereby leading to higher user connectivity rate and comparable average spectral efficiency. This innovative approach sheds light on the potential of metaheuristic algorithms in tackling intricate UA challenges, offering valuable insights for the future design and optimization of mobile networks.