Transcriptional regulator with bimodal DNA-binding specificity. Binds with a higher affinity to methylated CpG dinucleotides in the consensus sequence 5'-CGCG-3' but can also bind to E-box elements (5'-CACGTG-3'). Can also bind specifically to a single methyl-CpG pair. Represses transcription in a methyl-CpG-dependent manner (PubMed:16354688). Plays an important role in regulating DNA replication and common fragile sites (CFS) stability in a RBBP6- and MCM10-dependent manner; represses expression of MCM10 which plays an important role in DNA-replication (PubMed:24726359). Acts as a transcriptional activator. May be involved in the differentiation and/or survival of late postmitotic neurons (By similarity). {ECO:0000250|UniProtKB:Q5EXX3, ECO:0000269|PubMed:16354688, ECO:0000269|PubMed:24726359}. This is the function of ZBTB38 (zinc finger and BTB domain containing 38, Ensembl gene identifier ENSG00000177311).