Deploying quantized deep neural network (DNN) models with resource adaptation capabilities on ubiquitous Internet of Things (IoT) devices to provide high-quality AI services can leverage the benefits of compression and meet multi-scenario resource requirements. However, existing dynamic/mixed precision quantization requires retraining or special hardware, whereas post-training quantization (PTQ) has two limitations for resource adaptation: (i) The state-of-the-art PTQ methods only provide one fixed bitwidth model, which makes it challenging to adapt to the dynamic resources of IoT devices; (ii) Deploying multiple PTQ models with diverse bitwidths consumes large storage resources and switching overheads. To this end, this paper introduces a resource-friendly post-training integer-nesting quantization, i.e., NestQuant, for on-device quantized model switching on IoT devices. The proposed NestQuant incorporates the integer weight decomposition, which bit-wise splits quantized weights into higher-bit and lower-bit weights of integer data types. It also contains a decomposed weights nesting mechanism to optimize the higher-bit weights by adaptive rounding and nest them into the original quantized weights. In deployment, we can send and store only one NestQuant model and switch between the full-bit/part-bit model by paging in/out lower-bit weights to adapt to resource changes and reduce consumption. Experimental results on the ImageNet-1K pretrained DNNs demonstrated that the NestQuant model can achieve high performance in top-1 accuracy, and reduce in terms of data transmission, storage consumption, and switching overheads. In particular, the ResNet-101 with INT8 nesting INT6 can achieve 78.1% and 77.9% accuracy for full-bit and part-bit models, respectively, and reduce switching overheads by approximately 78.1% compared with diverse bitwidths PTQ models.