In this paper, to deal with the heterogeneity in federated learning (FL) systems, a knowledge distillation (KD) driven training framework for FL is proposed, where each user can select its neural network model on demand and distill knowledge from a big teacher model using its own private dataset. To overcome the challenge of train the big teacher model in resource limited user devices, the digital twin (DT) is exploit in the way that the teacher model can be trained at DT located in the server with enough computing resources. Then, during model distillation, each user can update the parameters of its model at either the physical entity or the digital agent. The joint problem of model selection and training offloading and resource allocation for users is formulated as a mixed integer programming (MIP) problem. To solve the problem, Q-learning and optimization are jointly used, where Q-learning selects models for users and determines whether to train locally or on the server, and optimization is used to allocate resources for users based on the output of Q-learning. Simulation results show the proposed DT-assisted KD framework and joint optimization method can significantly improve the average accuracy of users while reducing the total delay.