The deployment of the Internet of Things (IoT) in smart cities and critical infrastructure has enhanced connectivity and real-time data exchange but introduced significant security challenges. While effective, cryptography can often be resource-intensive for small-footprint resource-constrained (i.e., IoT) devices. Radio Frequency Fingerprinting (RFF) offers a promising authentication alternative by using unique RF signal characteristics for device identification at the Physical (PHY)-layer, without resorting to cryptographic solutions. The challenge is two-fold: how to deploy such RFF in a large scale and for resource-constrained environments. Edge computing, processing data closer to its source, i.e., the wireless device, enables faster decision-making, reducing reliance on centralized cloud servers. Considering a modest edge device, we introduce two truly lightweight Edge AI-based RFF schemes tailored for resource-constrained devices. We implement two Deep Learning models, namely a Convolution Neural Network and a Transformer-Encoder, to extract complex features from the IQ samples, forming device-specific RF fingerprints. We convert the models to TensorFlow Lite and evaluate them on a Raspberry Pi, demonstrating the practicality of Edge deployment. Evaluations demonstrate the Transformer-Encoder outperforms the CNN in identifying unique transmitter features, achieving high accuracy (> 0.95) and ROC-AUC scores (> 0.90) while maintaining a compact model size of 73KB, appropriate for resource-constrained devices.