In this study, A Quantum-Classical Federated Learning (QCFL) framework designed for skin cancer prediction is presented. It integrates classical convolutional neural networks with variational quantum circuits so that both quantum computing and deep learning can be used in decentralized, privacy-preserving environments. The functioning of the Federated Learning model includes a efficient optimization algorithm suitable for quantum environments in FL called SCAFFOLD, which handle client heterogeneity and non-IID data distributions modeled using Dirichlet sampling. The framework includes three ways of training normal training along with trigger-based and semantic-based backdoor attacks to understand demonstrating the susceptibility of federated skin cancer models to stealthy adversarial behaviors. To defend against such threats, multiple detection and mitigation strategies are evaluated, including Activation Clustering, Neural Cleanse, and Fine-Pruning. . Additionally, a novel approach for defense, Spectral Defense, is proposed and developed, based on the eigen-spectrum analysis of internal neural activations to detect and ultimately suppress backdoor behavior without recourse to clean validation data. Experimental results on this hybrid quantum-classical model prove improvement in classification performance, whereas the Spectral Defense framework provides significant attack success rates reduction with little degradation in model accuracy. This work provides a robust and scalable approach for deploying secure federated learning systems to adverse conditions for medical image analysis.