The surge in counterfeit signatures has inflicted widespread inconveniences and formidable challenges for both individuals and organizations. This groundbreaking research paper introduces SigScatNet, an innovative solution to combat this issue by harnessing the potential of a Siamese deep learning network, bolstered by Scattering wavelets, to detect signature forgery and assess signature similarity. The Siamese Network empowers us to ascertain the authenticity of signatures through a comprehensive similarity index, enabling precise validation and comparison. Remarkably, the integration of Scattering wavelets endows our model with exceptional efficiency, rendering it light enough to operate seamlessly on cost-effective hardware systems. To validate the efficacy of our approach, extensive experimentation was conducted on two open-sourced datasets: the ICDAR SigComp Dutch dataset and the CEDAR dataset. The experimental results demonstrate the practicality and resounding success of our proposed SigScatNet, yielding an unparalleled Equal Error Rate of 3.689% with the ICDAR SigComp Dutch dataset and an astonishing 0.0578% with the CEDAR dataset. Through the implementation of SigScatNet, our research spearheads a new state-of-the-art in signature analysis in terms of EER scores and computational efficiency, offering an advanced and accessible solution for detecting forgery and quantifying signature similarities. By employing cutting-edge Siamese deep learning and Scattering wavelets, we provide a robust framework that paves the way for secure and efficient signature verification systems.