The Wizengamot Administration Services is an office located on Level 2 of the Ministry of Magic headquarters, as part of the Department of Magical Law Enforcement, which undertakes administrative and clerical duties for the Wizengamot. Its functions seem analogous to Muggle court registries; this would typically include maintenance of court documents, hearing dates, judges' schedules, and the administration of legal proceedings.

Department of Magical Law Enforcement
Level 2, Ministry of Magic
Auror Office · Department of Intoxicating Substances · Improper Use of Magic Office · Misuse of Muggle Artefacts Office · Office for the Detection and Confiscation of Counterfeit Defensive Spells and Protective Objects · Magical Law Enforcement Patrol · Hit Wizards · Ministry of Magic Witch Watchers · Department of Magical Equipment Control · Administrative Registration Department · Wizengamot Administration Services · Department of Security · Animagus Registry