Fdroid with private list

Is possible I to create a fdroid.apk that list just apps of a specific public hosting?

Definitely. fdroidclient is designed to be “white labeled”, i.e. to make custom builds that can be reconfigured and rebranded. We also do consulting for hire for that kind of thing.

https://f-droid.org/docs/Whitelabel_Builds/

Ok, in this case I need to do a download of fdroid and create a new embedded with this function, ok?
And I need alter the configurations to get the specifics repositories?

“Whitelabel” means making a custom build. So you’ll need to get the source code and change the configuration there. Then make and release your own build.