Federated Learning (FL) plays a critical role in distributed systems. In these systems, data privacy and confidentiality hold paramount importance, particularly within edge-based data processing systems such as IoT devices deployed in smart homes. FL emerges as a privacy-enforcing sub-domain of machine learning that enables model training on client devices, eliminating the necessity to share private data with a central server. While existing research has predominantly addressed challenges pertaining to data heterogeneity, there remains a current gap in addressing issues such as varying device capabilities and efficient communication. These unaddressed issues raise a number of implications in resource-constrained environments. In particular, the practical implementation of FL-based IoT or edge systems is extremely inefficient. In this paper, we propose "Resource-Efficient Federated Training Framework for Heterogeneous and Resource-Constrained Environments (REFT)," a novel approach specifically devised to address these challenges in resource-limited devices. Our proposed method uses Variable Pruning to optimize resource utilization by adapting pruning strategies to the computational capabilities of each client. Furthermore, our proposed REFT technique employs knowledge distillation to minimize the need for continuous bidirectional client-server communication. This achieves a significant reduction in communication bandwidth, thereby enhancing the overall resource efficiency. We conduct experiments for an image classification task, and the results demonstrate the effectiveness of our approach in resource-limited settings. Our technique not only preserves data privacy and performance standards but also accommodates heterogeneous model architectures, facilitating the participation of a broader array of diverse client devices in the training process, all while consuming minimal bandwidth.