Advancements in technology have heightened concerns over personal privacy and security. Electroencephalogram (EEG) signals, valued for their unique and non-forgeable characteristics, have garnered increasing interest for biometric verification. Yet challenges persist in real-world applications, including poor performance in cross-session recognition, lack of generalizability, and narrow focus on specific EEG elicitation protocols. In this paper, we propose a deep learning-based EEG biometric verification system. Our approach introduces advancements in feature extraction: starting with Fast Fourier Transform (FFT) for converting signals to frequency domain, followed by feature mining through a convolutional autoencoder. User verification is accomplished using a Convolutional Neural Network (CNN), known for its superior performance in data mining and classification tasks. In addition, to evaluate the generalizability of the proposed method, extensive experiments are carried out with EEG data collected under seven distinct signal elicitation protocols and over two different recording sessions. Results highlight the stability and reliability of the our method cross diverse scenarios. Comparative analysis with state-of-the-art approaches for EEG biometrics shows that our method excels in robust feature extraction, resulting in better verification performance.