Our approach effectively manages heterogeneous environments, accommodating differences in client computational capabilities, data distributions, and communication delays, making it suitable for real-world Federated Learning applications. We also analyze the effects of client selection methods—specifically, choosing clients with or without replacement—on variance and model convergence, providing insights for more effective sampling strategies. The practical implementation of our methods using PyTorch and Python’s asyncio library demonstrates their applicability in real-world asynchronous and heterogeneous FL scenarios. Empirical experiments validate the proposed methods, showing improved performance and scalability in handling asynchronous updates, and non-convex client’s objective function with associated heterogeneous dataset.