Users can search artifacts under trash can using the UI following our document here.
Also, users can use the File List REST API against 'auto-trashcan' to search for items under trash can.
For example:
curl -uuser:pwd https://ARTIFACTORY_URL/artifactory/api/storage/auto-trashcan
With this API, the below filters can be added according to the user’s need.
/{folder-path}?list[&deep=0/1][&depth=n][&listFolders=0/1][&mdTimestamps=0/1][&includeRootPath=0/1]