Despite the advantage of preserving data privacy, federated learning (FL) still suffers from the straggler issue due to the limited computing resources of distributed clients and the unreliable wireless communication environment. By effectively imitating the distributed resources, digital twin (DT) shows great potential in alleviating this issue. In this paper, we leverage DT in the FL framework over non-orthogonal multiple access (NOMA) network to assist FL training process, considering malicious attacks on model updates from clients. A reputationbased client selection scheme is proposed, which accounts for client heterogeneity in multiple aspects and effectively mitigates the risks of poisoning attacks in FL systems. To minimize the total latency and energy consumption in the proposed system, we then formulate a Stackelberg game by considering clients and the server as the leader and the follower, respectively. Specifically, the leader aims to minimize the energy consumption while the objective of the follower is to minimize the total latency during FL training. The Stackelberg equilibrium is achieved to obtain the optimal solutions. We first derive the strategies for the followerlevel problem and include them in the leader-level problem which is then solved via problem decomposition. Simulation results verify the superior performance of the proposed scheme.