I tried doing an ajax call with the local path "ms-appx-web:///www//demo_data//demo.json".
Firstly, the ms-appx-web scheme may not be supported by jQuery.ajax(). Actually it is invoke the  XMLHttpRequest, the request need to be  XMLHTTPRequest standard. If you invoke the ajax call with ms-appx-web in a HTML directly you will get the error details:
jquery-3.2.1.min.js:4 XMLHttpRequest cannot load ms-appx-web:///test.json. Cross origin requests are only supported for protocol schemes: http, data, chrome, chrome-extension, https.
So secondly, the file should be in a web server. A local file may not be loaded by this method. And the uwp app is not a web server you may not use jQuery.ajax() to load the local file.
If you just want to show the json file inside the WebView, there're several ways you may reference.
- Upload to a web server and use the jQuery.ajax().
- Load the Json file by uwp APIs and then load it by  - NavigateToStringmethod. For example(parse the json if needed):
 - StorageFile f = await StorageFile.GetFileFromApplicationUriAsync(new Uri("ms-appx:///Assets/www/test.json"));
WebBrowser.NavigateToString(await FileIO.ReadTextAsync(f));
 
- Hard code the content of json file directly inside the js as an object for dealing. For example: - <script type='text/javascript'> 
    function doSomething() {
        var data = '[{"name" : "Ashwin", "age" : "20"},{"name" : "Abhinandan", "age" : "20"}]';
        var mydata = JSON.parse(data);             
        document.getElementById('myDiv').innerText ="name:"+ mydata[0].name;
        return "done";
    }
</script> 
//Invoke the script by webview
private async void btninvoke_Click(object sender, RoutedEventArgs e)
{
    string result = await WebBrowser.InvokeScriptAsync("doSomething", null);
}
 
More details please reference this thread, and more details about the WebView please reference the official sample.