Hello,

Adding some results from our email discussion.
The CMS.File documents have the file extension stored in the DocumentExtensions field, you can use two parameters, classnames for "cms.file" and where condition with actual file extensions filtering.

Following REST query works for me in testing setup with sample Corporate site to select png and gif files:

~/rest/content/site/corporatesite/en-us/childrenof?classnames=cms.file&where=documentextensions%20IN%20(%27.gif%27,%27.png%27)

The childrenof expression helps to avoid /all, although in case of specified site and document query, you should be able to use /all even for non-admins. Classnames parameter then helps to narrow the search in the specified document types only. You can separate multiple classnames by comma.

Hope this will help.

Regards,
Zdenek