The edge-device environment imposes severe resource limitations, encompassing computation costs, hardware resource usage, and energy consumption for deploying deep neural network models. Ultra-low-bit quantization and hardware accelerators have been explored as promising approaches to address these challenges. Ultra-low-bit quantization significantly reduces the model size and the computational cost. Despite progress so far, many competitive ultra-low-bit models still partially rely on float or non-ultra-low-bit quantized computation such as the input and output layer. We introduce Efficiera Residual Networks (ERNs), a model optimized for low-resource edge devices. ERNs achieve full ultra-low-bit quantization, with all weights, including the initial and output layers, being binary, and activations set at 2 bits. We introduce the shared constant scaling factor technique to enable integer-valued computation in residual connections, allowing our model to operate without float values until the final convolution layer. Demonstrating competitiveness, ERNs achieve an ImageNet top-1 accuracy of 72.5pt with a ResNet50-compatible architecture and 63.6pt with a model size less than 1MB. Moreover, ERNs exhibit impressive inference times, reaching 300FPS with the smallest model and 60FPS with the largest model on a cost-efficient FPGA device.