Quantized Neural Networks (QNNs) are increasingly deployed in edge and resource-constrained environments due to their efficiency in computation and memory usage. While shown to distort the gradient landscape and weaken conventional pixel-level attacks, it provides limited robustness against patch-based adversarial attacks-localized, high-saliency perturbations that remain surprisingly transferable across bit-widths. Existing defenses either overfit to fixed quantization settings or fail to address this cross-bit generalization vulnerability. We introduce \textbf{TriQDef}, a tri-level quantization-aware defense framework designed to disrupt the transferability of patch-based adversarial attacks across QNNs. TriQDef consists of: (1) a Feature Disalignment Penalty (FDP) that enforces semantic inconsistency by penalizing perceptual similarity in intermediate representations; (2) a Gradient Perceptual Dissonance Penalty (GPDP) that explicitly misaligns input gradients across bit-widths by minimizing structural and directional agreement via Edge IoU and HOG Cosine metrics; and (3) a Joint Quantization-Aware Training Protocol that unifies these penalties within a shared-weight training scheme across multiple quantization levels. Extensive experiments on CIFAR-10 and ImageNet demonstrate that TriQDef reduces Attack Success Rates (ASR) by over 40\% on unseen patch and quantization combinations, while preserving high clean accuracy. Our findings underscore the importance of disrupting both semantic and perceptual gradient alignment to mitigate patch transferability in QNNs.