As machine learning inferences increasingly move to edge devices, adapting to diverse computational capabilities, hardware, and memory constraints becomes more critical. Instead of relying on a pre-trained model fixed for all future inference queries across diverse edge devices, we argue that planning an inference pattern with a request-specific model tailored to the device's computational capacity, accuracy requirements, and time constraints is more cost-efficient and robust to diverse scenarios. To this end, we propose an accuracy-aware and workload-balanced inference system that integrates joint model quantization and inference partitioning. In this approach, the server dynamically responds to inference queries by sending a quantized model and adaptively sharing the inference workload with the device. Meanwhile, the device's computational power, channel capacity, and accuracy requirements are considered when deciding. Furthermore, we introduce a new optimization framework for the inference system, incorporating joint model quantization and partitioning. Our approach optimizes layer-wise quantization bit width and partition points to minimize time consumption and cost while accounting for varying accuracy requirements of tasks through an accuracy degradation metric in our optimization model. To our knowledge, this work represents the first exploration of optimizing quantization layer-wise bit-width in the inference serving system, by introducing theoretical measurement of accuracy degradation. Simulation results demonstrate a substantial reduction in overall time and power consumption, with computation payloads decreasing by over 80% and accuracy degradation kept below 1%.