Designing an end-to-end deep learning network to match the biometric features with limited training samples is an extremely challenging task. To address this problem, we propose a new way to design an end-to-end deep CNN framework i.e., PVSNet that works in two major steps: first, an encoder-decoder network is used to learn generative domain-specific features followed by a Siamese network in which convolutional layers are pre-trained in an unsupervised fashion as an autoencoder. The proposed model is trained via triplet loss function that is adjusted for learning feature embeddings in a way that minimizes the distance between embedding-pairs from the same subject and maximizes the distance with those from different subjects, with a margin. In particular, a triplet Siamese matching network using an adaptive margin based hard negative mining has been suggested. The hyper-parameters associated with the training strategy, like the adaptive margin, have been tuned to make the learning more effective on biometric datasets. In extensive experimentation, the proposed network outperforms most of the existing deep learning solutions on three type of typical vein datasets which clearly demonstrates the effectiveness of our proposed method.