Is it possible to keep arcgis server on local network and access its services through a web application on internet. Is there a way to make local network services available to application on internet.
You may be interested in setting up a distributed collaboration to copy and sync items from ArcGIS Enterprise to ArcGIS Online. The feature layers would be copied to ArcGIS Online and thus accessible over the internet. The application would need a way to authenticate users (such as Named User logins) if the copied layer is not shared with everyone.
This link offers more information about what types of items can be shared via collaboration.