Air-writing signature authentication is a form of biometric authentication that verifies an individual’s identity using their physical characteristics and behavioral patterns. In recent years, many researchers have been studying aerial signature authentication using various devices and deep neural network techniques. However, limited sample sizes in datasets have often resulted in insufficient accuracy. In this regard, we proposed a deep learning (DL) based in-air signature authentication system using 3D depth camera. We constructed a custom air signature collection system using a 3D depth camera called OAK-D, enabling us to gather a total of 660 signatures. The Siamese network addresses the traditional issue of dataset scarcity and allows for sufficient training sample sizes. We employed LSTM and Bi-LSTM based DL model for user authentication. We trained our proposed system with fivefold cross-validation and repeated their model performances into five times. Our experimental results showed that our proposed system obtained a equal error rate of 2.41%.