This article conducts a comprehensive analysis of the inter-generational correlation between parent and child fingerprints, utilizing advanced image processing techniques and machine learning. Fingerprint patterns, known for their individuality, often exhibit hereditary traits within families. We employ Gray Label Co-Occurrence Matrix (GLCM) characteristics that draw out from fingerprint images in four directions to quantify textural patterns. Our dataset includes fingerprint samples from 100 families in West Bengal, India, covering both parents and children. Our primary objective is to quantify the similarity between parent-child fingerprint patterns, shedding light on potential hereditary characteristics. We employ a Random Forest classifier, renowned for capturing complex data relationships, to classify fingerprint pairs as related or unrelated, establishing a correlation between the two. Our results show the effectiveness of our approach, with a training precision of 97% with a validation precision of 82%. These findings highlight significant inter-generational correlations in fingerprint patterns, suggesting a genetic component in fingerprint traits.