Transcription factor (TF) proteins play a critical role in the regulation of eukaryote gene expression via sequence-specific binding to genomic locations known as TF binding sites. We studied sites of genomic variation between modern human and Neanderthal promoters. We detected significant differences in the binding affinities of 110 TFs to the promoters of 75 target genes. The TFs were enriched for terms related to vision, motor neurons, homeobox, and brain, whereas the target genes and their direct interactors were enriched in terms related to autism, brain, connective tissue, trachea, prostate, skull morphology, and vision. Secondary analysis of single-cell data revealed that a subset of the identified TFs (CUX1, CUX2, ESRRG, FOXP1, FOXP2, MEF2C, POU6F2, PRRX1 and RORA) co-occur as marker genes in L4 glutamatergic neurons. The majority of these genes have known roles in autism and/or schizophrenia and are associated with human accelerated regions (elevated divergence in humans vs. other primates). Analysis of a single-nucleus dataset of cortical tissue showed that 15 of these TFs and 16 of their target genes are differentially expressed in autism vs. control, most commonly upregulated in developing neurons. Down regulation of these genes occurred in SV2C- and somatostatin-expressing interneurons, oligodendrocytes, and oligodendrocyte precursor cells. These results support the value of gene regulation studies for the evolution of human cognitive abilities and the neuropsychiatric disorders that accompany it.