All records for Jan Mayen at DigitalArkivet (Digital Archives of Norway) are free. Online Jan Mayen Genealogy Records can be searched by person, property, or record type.
Search by property/residential here as of date of this listing there were no property records online
For property searches AND record type searches, you’ll want to refine your search by Geography, then Svalbard, then Jan Mayen.
When searching by record type (Category|Kategori), you can search ALL record types by refining the Geography to Jan Mayen, select 2211 Jan Mayen, and then select Search.