Acts as a negative regulator of the Wnt signaling pathway via its interaction with DVL1 (By similarity). Binds preferentially to DNA containing cytidine-phosphate-guanosine (CpG) dinucleotides over CpH (H=A, T, and C), hemimethylated-CpG and hemimethylated-hydroxymethyl- CpG (PubMed:29276034). {ECO:0000250|UniProtKB:Q6NXI8, ECO:0000269|PubMed:29276034}. This is the function of Ensembl gene identifier ENSG00000168772 (CXXC4, CXXC finger protein 4).