Vision Transformers and Deep Neural Networks have been widely used for image classification task but deploying them on resource-constrained edge devices presents significant challenges due to their high computational demands. To address this, we employed the lightweight MobileNetV4 model, enhanced with advanced features such as the Universal Inverted Bottleneck and Mobile Multi-Query Attention, for heritage site classification on the Indian Heritage Digital Space Dataset. A comparative analysis was conducted between MobileNetV4 and MobileNetV3, both trained on the IHDS dataset, by applying 4-bit and 6-bit Post-training Quantization. MobileNetV4, with an original model size of 33.99 MB, was compressed to 5.38 MB using 6-bit quantization and further reduced to 4.05 MB with 4-bit quantization, achieving accuracies of 91.47 and 88.62%, respectively. In contrast, MobileNetV3, with an original model size of 20.9 MB, experienced greater accuracy loss after quantization, with 6-bit and 4-bit accuracies of 87.50 and 82.30%, and corresponding model sizes of 4.39 and 2.68 MB. These results demonstrate that MobileNetV4 outperforms MobileNetV3 in maintaining accuracy post-quantization while achieving significant model size reduction. This highlights MobileNetV4 as an efficient and practical choice for deploying heritage site classification models on edge devices.