Studying the early dynamic development of cortical folding with remarkable individual variability is critical for understanding normal early brain development and related neurodevelopmental disorders. This study focuses on the fingerprinting capability and the individual variability of cortical folding during early brain development. Specifically, we aim to explore (a) whether the developing neonatal cortical folding is unique enough to be considered as a "fingerprint" that can reliably identify an individual within a cohort of infants; (b) which cortical regions manifest more individual variability and thus contribute more for infant identification; (c) whether the infant twins can be distinguished by cortical folding. Hence, for the first time, we conduct infant individual identification and individual variability analysis involving twins based on the developing cortical folding features (mean curvature, average convexity, and sulcal depth) in 472 neonates with 1,141 longitudinal MRI scans. Experimental results show that the infant individual identification achieves 100% accuracy when using the neonatal cortical folding features to predict the identities of 1- and 2-year-olds. Besides, we observe high identification capability in the high-order association cortices (i.e., prefrontal, lateral temporal, and inferior parietal regions) and two unimodal cortices (i.e., precentral gyrus and lateral occipital cortex), which largely overlap with the regions encoding remarkable individual variability in cortical folding during the first 2 years. For twins study, we show that even for monozygotic twins with identical genes and similar developmental environments, their cortical folding features are unique enough for accurate individual identification; and in some high-order association cortices, the differences between monozygotic twin pairs are significantly lower than those between dizygotic twins. This study thus provides important insights into individual identification and individual variability based on cortical folding during infancy.