During the 3rd trimester, the human brain undergoes rapid cellular and molecular processes that reshape the structural architecture of the cerebral cortex. Knowledge of cortical differentiation obtained predominantly from histological studies is limited in localized and small cortical regions. How cortical microstructure is differentiated across cortical regions in this critical period is unknown. In this study, the cortical microstructural architecture across the entire cortex was delineated with non-Gaussian diffusion kurtosis imaging as well as conventional diffusion tensor imaging of 89 preterm neonates aged 31-42 postmenstrual weeks. The temporal changes of cortical mean kurtosis (MK) or fractional anisotropy (FA) were heterogeneous across the cortical regions. Cortical MK decreases were observed throughout the studied age period while cortical FA decrease reached its plateau around 37 weeks. More rapid decreases in MK were found in the primary visual region while faster FA declines were observed in the prefrontal cortex. We found that distinctive cortical microstructural changes were coupled with microstructural maturation of associated white matter tracts. Both cortical MK and FA measurements predicted the postmenstrual age of preterm infants accurately. This study revealed a differential 4D spatiotemporal cytoarchitectural signature inferred by non-Gaussian diffusion barriers inside the cortical plate during the 3rd trimester. The cytoarchitectural processes, including dendritic arborization and neuronal density decreases, were inferred by regional cortical FA and MK measurements. The presented findings suggest that cortical MK and FA measurements could be used as effective imaging markers for cortical microstructural changes in typical and potentially atypical brain development.