Deepfakes represent one of the toughest challenges in the world of Cybersecurity and Digital Forensics, especially considering the high-quality results obtained with recent generative AI-based solutions. Almost all generative models leave unique traces in synthetic data that, if analyzed and identified in detail, can be exploited to improve the generalization limitations of existing deepfake detectors. In this paper we analyzed deepfake images in the frequency domain generated by both GAN and Diffusion Model engines, examining in detail the underlying statistical distribution of Discrete Cosine Transform (DCT) coefficients. Recognizing that not all coefficients contribute equally to image detection, we hypothesize the existence of a unique ``discriminative fingerprint", embedded in specific combinations of coefficients. To identify them, Machine Learning classifiers were trained on various combinations of coefficients. In addition, the Explainable AI (XAI) LIME algorithm was used to search for intrinsic discriminative combinations of coefficients. Finally, we performed a robustness test to analyze the persistence of traces by applying JPEG compression. The experimental results reveal the existence of traces left by the generative models that are more discriminative and persistent at JPEG attacks.