Explanation:
Modifications can occur on both DNA and proteins, which regulate various cellular processes such as DNA replication, transcription, protein localization, and degradation. Among the modifications mentioned in the given options, only methylation occurs on both DNA and protein.

Methylation:
Methylation is a post-translational modification that occurs on both DNA and protein. The addition of a methyl group (-CH3) to the DNA base cytosine by DNA methyltransferases (DNMTs) is called DNA methylation. It is an epigenetic modification that regulates gene expression by inhibiting transcription. In protein, methylation occurs on the side chains of amino acids such as lysine, arginine, and histidine. The addition of a methyl group to a protein can affect its structure, function, and stability.

Other modifications:
The other modifications mentioned in the options occur either on DNA or protein, but not on both.

- ADP-ribosylation: It is a modification that occurs on proteins, where an ADP-ribose group is added to an amino acid residue. This modification regulates various cellular processes such as DNA repair, transcription, and apoptosis.
- Sumoylation: This modification occurs on proteins, where a Small Ubiquitin-like Modifier (SUMO) protein is added to a lysine residue. It regulates protein localization, transcription, and DNA repair.
- Ubiquitination: It is a modification that occurs on proteins, where a ubiquitin protein is added to a lysine residue. This modification marks the protein for degradation by the proteasome.

Conclusion:
In conclusion, among the given options, only methylation occurs on both DNA and protein. Methylation regulates gene expression by inhibiting transcription in DNA and affects protein structure, function, and stability in proteins.