How to publish in internet only the files modified in the Sitely app to the Internet and not the entire site with each modification?
I think it already is.
A lot of talk about this topic in the forum, including Duncan has explained it several times…
From what I understand if you move an element on your canvas Sitely also has to adjust the CSS. Changing text is somewhat simpler (unless the container is expanded). So overall Sitely will always update your changes (not the entire site) but it will also update the code supporting the changes.
And remember making changes on your desktop interacts with your mobile device to an extent so more than just the desktop update occurs.