The fingerprint verification system is widely used in mobile devices because of fingerprint's distinctive features and ease of capture. Typically, mobile devices utilize small sensors, which have limited area, to capture fingerprint. Meanwhile, conventional fingerprint feature extraction methods need detailed fingerprint information, which is unsuitable for those small sensors. This paper proposes a novel fingerprint verification method for small area sensors based on deep learning. A systematic method combines deep convolutional neural network (DCNN) in a Siamese network for feature extraction and XGBoost for fingerprint similarity training. In addition, a padding technique also introduced to avoid wraparound error problem. Experimental results show that the method achieves an improved accuracy of 66.6% and 22.6% in the FingerPassDB7 and FVC2006DB1B dataset, respectively, compared to the existing methods.