Traditional biometric systems have encountered significant setbacks due to various unavoidable factors, for example, wearing of face masks in face recognition-based biometrics and hygiene concerns in fingerprint-based biometrics. This paper proposes a novel lightweight vision transformer with phase-only cross-attention (POC-ViT) using dual biometric traits of forehead and periocular portions of the face, capable of performing well even with face masks and without any physical touch, offering a promising alternative to traditional methods. The POC-ViT framework is designed to handle two biometric traits and to capture inter-dependencies in terms of relative structural patterns. Each channel consists of a Cross-Attention using phase-only correlation (POC) that captures both their individual and correlated structural patterns. The computation of cross-attention using POC extracts the phase correlation in the spatial features. Therefore, it is robust against variations in resolution and intensity, as well as illumination changes in the input images. The lightweight model is suitable for edge device deployment. The performance of the proposed framework was successfully demonstrated using the Forehead Subcutaneous Vein Pattern and Periocular Biometric Pattern (FSVP-PBP) database, having 350 subjects. The POC-ViT framework outperformed state-of-the-art methods with an outstanding classification accuracy of $98.8\%$ with the dual biometric traits.