Traditionally, federated learning (FL) aims to train a single global model while collaboratively using multiple clients and a server. Two natural challenges that FL algorithms face are heterogeneity in data across clients and collaboration of clients with diverse resources. In this work, we introduce a quantized and personalized FL algorithm QuPeD that facilitates collective (personalized model compression) training via knowledge distillation (KD) among clients who have access to heterogeneous data and resources. For personalization, we allow clients to learn compressed personalized models with different quantization parameters and model dimensions/structures. Towards this, first we propose an algorithm for learning quantized models through a relaxed optimization problem, where quantization values are also optimized over. When each client participating in the (federated) learning process has different requirements of the compressed model (both in model dimension and precision), we formulate a compressed personalization framework by introducing knowledge distillation loss for local client objectives collaborating through a global model. We develop an alternating proximal gradient update for solving this compressed personalization problem, and analyze its convergence properties. Numerically, we validate that QuPeD outperforms competing personalized FL methods, FedAvg, and local training of clients in various heterogeneous settings.