You are right that the Web API has no aspx, it is for the most part all files in the BIN folder.
I will try to deploy it manually (as I do when installing on customer web servers). I know I can deploy it from the VS to the local drive. But I am concerned of messing up something on the DiscountASP site. Now that I am thinking about it, the important for me is to have the web.config in a separate sub-folder so that it won't conflict with the existing web.config.
Thank you.

>Web API projects are based on MVC and don't have aspx files, so not sure what you have there.
>
>You should be able to right-click on the project in VS and select Deploy from there.
>
>
>>Hi,
>>
>>When I asked the DiscountASP tech support (via email) if I can deploy a Web API to my current site, they said Yes. But not much more, as far as details. I am sure they think it is so simple that does not require explanation. But I need some help.
>>
>>I connect to my site (hosted by DiscountASP.net) using FileZilla. When I connect I see the root directory and many sub-directories that I created (for various purposes). Say I want to manually copy and deploy the Web API project. Currently I have this Web API set as a web project with just a couple of file (e.g. Global.aspx, web.config, packages.config) and many files in the BIN folder.
>>Would I copy these files to the DiscountASP.NET site the same way?: some files to the root folder and then all files in my BIN folder to the hosted BIN folder?
>>What if I want to separate this Web API in its own folder (rather than placing all file to the Root folder), can and how do I do it?
>>
>>TIA