Hey,
There are a lot of ways to test this, so it depends. You'll need to be aware of what actually causes the download, then think of a way to test that mechanism.
If your server sends specific disposition headers which cause a browser to prompt for download, you can figure out what URL this request is made to, and use 'cy.request()' to hit that directly. Then you can test that the server send the right response headers.
If it's an anchor that initiates the download, you could test that it has the right href property. As long as you can verify that clicking the button is going to make the right HTTP request, that might be enough to test for.