With the deepening trend of paperless workflows, signatures as a means of identity authentication are gradually shifting from traditional ink-on-paper to electronic formats.Despite the availability of dynamic pressure-sensitive and PKI-based digital signatures, static scanned signatures remain prevalent in practice due to their convenience. However, these static images, having almost lost their authentication attributes, cannot be reliably verified and are vulnerable to malicious copying and reuse. To address these issues, we propose AuthSig, a novel static electronic signature framework based on generative models and watermark, which binds authentication information to the signature image. Leveraging the human visual system's insensitivity to subtle style variations, AuthSig finely modulates style embeddings during generation to implicitly encode watermark bits-enforcing a One Signature, One Use policy.To overcome the scarcity of handwritten signature data and the limitations of traditional augmentation methods, we introduce a keypoint-driven data augmentation strategy that effectively enhances style diversity to support robust watermark embedding. Experimental results show that AuthSig achieves over 98% extraction accuracy under both digital-domain distortions and signature-specific degradations, and remains effective even in print-scan scenarios.