The sixth-generation (6G) wireless cellular network integrates several wireless bands and modes with the objectives of improving quality of service (QoS) and increasing network connectivity. The 6G environment includes asymmetrical heterogeneous networks (HetNets) with the intention of making effective use of the available frequencies. However, selecting a suitable gNB and a communication channel that works for users in the network is an enormous challenge in 6G HetNets. This paper investigates a joint user association (UA) and channel allocation (CA) problem in two-tier HetNets by considering the downlink scenario to improve QoS. Our study presents an innovative scheme for user association and channel allocation, wherein the user can be connected to either the macro base station (MBS) or a possible small base station (SBS) in a direct or relay-assisted link. Furthermore, the proposed scheme identifies the optimal channel to be allocated to each user so that the overall network QoS can be maximized. A symmetric matching game-based user association is proposed to find the optimal association for users. Moreover, a modified auction game is applied to allocate the optimal channel by considering the quota of each gNB. Regarding connection probability, throughput, energy efficiency (EE), and spectrum efficiency (SE), the simulation results show that the proposed approach performs well over the state-of-the-art techniques.