In this paper, we presented an evolutionary approach to dynamic signature verification. According to this approach, a genetic algorithm automates the development of a personalized convolutional neural network for each user of the biometric authentication system. The personalized convolutional neural network is adapted to individual biometric data of signature input dynamics. These data (coordinates of the pen tip, pressure, azimuth, tilt) are read when entering a signature using a graphics tablet. The effectiveness of the proposed biometric authentication method was studied on the MCYT_Signature_100 database. Note that our method achieved an equal error rate of 0.4%. This value exceeds the shared value of the non-personalized convolutional neural network architecture (the equal error rate was 1.6% on the same data). This demonstrates the superiority of evolutionary models personalized for each user in biometric identity authentication. To implement the proposed method, an intelligent system was implemented using Python, TensorFlow/Keras, and the Hugging Face platform. The developed intelligent system has the potential to be used in areas related to identity verification during banking operations, provision of government services, and in access control systems.