This functionality that existed in VS2012 for partial FTP publishing no longer exists, has been removed. I think only in Web Deploy it is still possible to do partial publishing according to modifications.
Another way would be to upload from outside VS (totally external, or even configured in a build step of a specific build configuration, for example RELEASE or create a unique configuration for publishing)
In this case you would have to create the scripts (it could be another VS project, a DLL that does the dirty work, it could be a PowerShell, Node.JS, etc) to do the validation of what was changed and to do the upload.
Here's an example using GULP (Node.js) to monitor changes: link
In this example, it monitors the files in real time, and every save modification, it sends the file (it can be catastrophic in the production environment, since you can change something to test and upload it in Understand well configured how to select only extensions / file types that pose no health risks to the application)