Abstract: Handwritten signature verification is vital for personal authentication across commercial and financial applications. Although deep learning methods are widely adopted for online signature verification (OSV), they often struggle with capturing highly discriminative features and modelling long-range dependencies. To address these issues, we propose a novel framework that integrates the augmented path signature (APS) descriptor with the T-Mamba model. The APS descriptor first applies time and basepoint augmentations, then computes sliding-window path signatures. The path signature is a non-parametric feature map from rough path theory that effectively captures geometric structures and nonlinear inter-channel interactions. Inspired by the efficacy of state space models (SSMs) in sequence modelling, our T-Mamba model employs a hybrid design combining two temporal convolutional network (TCN) blocks with a time-scanning Mamba. This design enables the model to learn both local temporal patterns and global long-range dependencies, substantially improving verification accuracy. Our framework achieves state-of-the-art EERs on three public benchmark datasets (MCYT-100, SVC-2004 Task 2, DeepSignDB), validating its effectiveness and robustness, especially when the training data is limited. Our code is publicly available at https://github.com/DLRL04/OSV-using-APS-and-T-Mamba.