The rapid expansion of 5G and IoT has increased security risks in e-health applications, where malware threats pose significant challenges to patient data protection. Traditional malware detection methods rely on conventional classifiers, limiting adaptability to evolving threats. This study introduces a deep learning-based malware detection approach utilizing Convolutional Neural Networks (CNNs) to enhance classification accuracy in e-health environments. A cascaded classification framework was developed, where an optimized AlexNet model in Stage-1 performs initial classification, followed by a Stage-2 three-tier classifier for fine-grained malware family detection. The performance of our approach was evaluated on the Malimg and Malvis datasets, which include 25 and 26 malware families, respectively. Experimental results demonstrate that the Stage-1 optimized AlexNet achieves 100% accuracy on Malimg and 93% on Malvis, outperforming standard AlexNet (96% and 88%), VGG16 (93% and 81%), and ResNet50 (85% and 79%). Future work will extend the cascaded classification framework by integrating the three-tier classifier results from Stage-2 to further improve detection precision.