There is no way to have the Publish Online files put on your server.
From what I've heard in5 is one of the best alternatives
In InDesign CC 2017 how do I get the files that Publish Online produces
To get to your files, use the dashboard. InDesign provides a Publish Online dashboard from where you can access all your published documents. To view the InDesign Publish Online dashboard, choose File > Publish Online Dashboard.
and put them on my server?
As per Steve, you can't host the files on your own server. This article does a really good job of explaining the exactly how Publish Online works, and there is a section devoted to embedding a published document on your own site.