Convert nested Json string to object and render in Jquery datatable cell

I think you are close. If you can rely on the text containing "InnerException" (if there is an inner exception, of course), then you can do something like this:

<script type="text/javascript">

let dataList = [{
        "id": 1,
        "Error": "Name missing in datatable"
    },
    {
        "id": 2,
        "Error": "{\"ErrorType\": \"401\", \"InnerException\":\"Invalid request, Please correct and submit\"}"
    }
];

  $(document).ready(function() {

    let RespTable = $('#dtResponse').DataTable( {
      data: dataList,
      columns: [
        { "title": "ID", "data": "id", "defaultContent": ""},
        { "title": "Error Message", "data": "Error", "defaultContent": "",
          "render": function (data, type) {
            if ( data.includes("InnerException") ) {
              let innerJson = JSON.parse(data);
              //console.log(innerJson);
              return innerJson.InnerException;
            } else {
              return data;
            }
          }
        }
      ]
    
  } );

} );

</script>

This uses data.includes("InnerException") as the test to see if it is OK to parse the string as JSON, or not.

The end result:

Update

A more rigorous approach is to add a function such as this:

function IsJsonString(str) {
    try {
        JSON.parse(str);
    } catch (e) {
        return false;
    }
    return true;
}

And then we can replace our string test with this:

if ( IsJsonString(data) ) {...}