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). Interacts with CBFA2T3. Interacts with ZBTB4. Interacts with RBBP6. Localizes to chromocenters. The BTB domain is not required for activation of transcription or self-association. Ubiquitinated by RBBP6; leading to its degradation by the proteasome. Genetic variations in ZBTB38 define the stature quantitative trait locus 10 (STQTL10) [MIM:612221]. Adult height is an easily observable and highly heritable complex continuous trait. Because of this, it is a model trait for studying genetic influence on quantitative traits.