how to bind the @html.dropdownlist name with id in mvc using JavaScript formate

change the type to GET in your ajax request like

 $.ajax({
 type: 'GET',
 ...

and try

$.each(data, function (index, val) {
    $('<option/>',{value:val.Id,text:val.Text}).appendTo("#MyDdl");
 });

You are sending a SelectList to the client. This class implements IEnumerable<SelectListItem> and SelectListItem has 2 properties: Value and Text which you should bind your drop down to:

$.ajax({
    type: 'POST',
    url: url,
    data: { id : id },
    success: function (data) {
        $('#MyDdl').empty();
        $.each(data, function () {
            $('#MyDdl').append(
                $('<option/>', {
                    value: this.Value,
                    html: this.Text
                })
            );
        });
    }
});

In your example you were using val.Id but there's no such property.

But as a matter of fact you don't need any SelectList. Just return the students collection:

[HttpPost]
public ActionResult Some(string id) 
{
    var students = service.GetAllStudents().ToList();
    students.Insert(0, new StudentModel{ Id = 0, Name = "Select student" });
    return Json(students);
}

and now you can bind your dropdown to the Id and Name properties of this collection:

$.each(data, function () {
    $('#MyDdl').append(
        $('<option/>', {
            value: this.Id,
            html: this.Name
        })
    );
});