Currently, as per Confluence Server REST API Documentation there is no API endpoint to download attachments from a Confluence page and we're only able to get a list of the attachments and their metadata.

For Confluence Cloud a new endpoint has been implemented, as per:

• New Download attachment REST API endpoint
• Get URI to download attachment

Which Redirects the client to a URL that serves an attachment's binary data, which can also be used to download attachments via OAuth 2 protocol.

It would be helpful to also have such endpoint implemented for on-premise deployments.