It depends on the needs of the mobile version. Often, a well designed responsive version of the same web app is enough. Even if it's a mobile native app, you might still be able to reuse some/most of the screens with the same html in a webview.
Even if you really needed it to be an API, you can always make the server side return either html or json depending on some request header. There's also a chance that the mobile version will be different enough from the desktop that it warrants new, custom built endpoints anyway.
