This paper proposes a novel federated algorithm that leverages momentum-based variance reduction with adaptive learning to address non-convex settings across heterogeneous data. We intend to minimize communication and computation overhead, thereby fostering a sustainable federated learning system. We aim to overcome challenges related to gradient variance, which hinders the model's efficiency, and the slow convergence resulting from learning rate adjustments with heterogeneous data. The experimental results on the image classification tasks with heterogeneous data reveal the effectiveness of our suggested algorithms in non-convex settings with an improved communication complexity of $\mathcal{O}(ε^{-1})$ to converge to an $ε$-stationary point - compared to the existing communication complexity $\mathcal{O}(ε^{-2})$ of most prior works. The proposed federated version maintains the trade-off between the convergence rate, number of communication rounds, and test accuracy while mitigating the client drift in heterogeneous settings. The experimental results demonstrate the efficiency of our algorithms in image classification tasks (MNIST, CIFAR-10) with heterogeneous data.