Federated recommendations leverage the federated learning (FL) techniques to make privacy-preserving recommendations. Though recent success in the federated recommender system, several vital challenges remain to be addressed: (i) The majority of federated recommendation models only consider the model performance and the privacy-preserving ability, while ignoring the optimization of the communication process; (ii) Most of the federated recommenders are designed for heterogeneous systems, causing unfairness problems during the federation process; (iii) The personalization techniques have been less explored in many federated recommender systems. In this paper, we propose a Communication efficient and Fair personalized Federated personalized Sequential Recommendation algorithm (CF-FedSR) to tackle these challenges. CF-FedSR introduces a communication-efficient scheme that employs adaptive client selection and clustering-based sampling to accelerate the training process. A fairness-aware model aggregation algorithm that can adaptively capture the data and performance imbalance among different clients to address the unfairness problems is proposed. The personalization module assists clients in making personalized recommendations and boosts the recommendation performance via local fine-tuning and model adaption. Extensive experimental results show the effectiveness and efficiency of our proposed method.