Palmprint recognition is an effective biometric authentication method, thanks to the unique patterns found in the inner palms of each person. Although traditional palmprint recognition systems can achieve impressive accuracies, they usually acquire a large number of labeled samples, which is time-consuming and costly to collect. In this chapter, we introduce an end-to-end algorithm for palmprint recognition using few-shot learning for small-sample, called MCI-Net (Mamba-Convolution Integration Network). Specifically, MCI-Net is trained episodically with a comprehensive framework to extract both global and local as well as channel and spatial features and take advantage of the effectiveness of Convolution and Mamba while maintaining suitable processing time for practical applications. Moreover, Mahalanobis is also utilized to assist the optimization to get the similarity scores between the support set and query image in few-shot condition. Adequate experiments carried out on contactless datasets prove that MCI-Net can achieve significant improvements compared to several state-of-the-art models.