There's no response because your code does not submit the Id.  If you were using debug tools like Dev Tools you should see errors.  Also if you set a break point in VS you'll notice the action is not hit.

IMHO, your filter design is a little confusing too.  Anyway, below is a basic example that builds my previous posts.

    public class HomeController : Controller
    {
        private readonly TestDbEntities context;
        public HomeController()
        {
            context = new TestDbEntities();
        }
        [HttpGet]
        public ActionResult Index()
        {
            var results = context.T_Projects;
            return View(results);
        }

        [HttpPost]
        public JsonResult Search(string Category)
        {
            //Projection query to populate the product view model
            List<ProductViewModel> products = (from prod in context.T_Projects
                                               where prod.T_ProjeCategory.KategoriAd == Category
                                               select new ProductViewModel()
                                               {
                                                   Baslik = prod.Baslik,
                                                   Icerik = prod.Icerik,
                                                   ProductId = prod.ID,
                                                   ResimYolu = prod.ResimYolu
                                               }).ToList();

            return Json(products);
        }

View

@model IEnumerable<MvcDbFirst.T_Projects>

@{
    ViewBag.Title = "Index";
}

<h2>Index</h2>

<div>
    <input type="text" name="Category" id="Category" />
    <input id="Search" type="button" value="Search" />
</div>
<hr />
<table class="table">
    <thead>
        <tr>
            <th>
                @Html.DisplayNameFor(model => model.Baslik)
            </th>
            <th>
                @Html.DisplayNameFor(model => model.Icerik)
            </th>
            <th>
                @Html.DisplayNameFor(model => model.ResimYolu)
            </th>
            <th>
                @Html.DisplayNameFor(model => model.T_ProjeCategory.KategoriAd)
            </th>
            <th></th>
        </tr>
    </thead>
    <tbody>
        @foreach (var item in Model)
        {
            <tr>
                <td>
                    @Html.DisplayFor(modelItem => item.Baslik)
                </td>
                <td>
                    @Html.DisplayFor(modelItem => item.Icerik)
                </td>
                <td>
                    @Html.DisplayFor(modelItem => item.ResimYolu)
                </td>
                <td>
                    @Html.DisplayFor(modelItem => item.T_ProjeCategory.KategoriAd)
                </td>
                <td>
                    @Html.ActionLink("Edit", "Edit", new { id = item.ID }) |
                    @Html.ActionLink("Details", "Details", new { id = item.ID }) |
                    @Html.ActionLink("Delete", "Delete", new { id = item.ID })
                </td>
            </tr>
        }
    </tbody>


</table>
@section scripts {
    <script>
        $('#Search').click(function () {
            var data = {
                Category: $('#Category').val()
            };

            $.ajax({
                type: 'POST',
                url: '@Url.Action("Search")',
                contentType: "application/json; charset=utf-8",
                dataType: 'json',
                data: JSON.stringify(data),
                success: function (response) {
                    console.log(response);
                }
            });
        });
    </script>
}

Model

    public class ProductViewModel
    {
        public int ProductId { get; set; }
        public string Baslik { get; set; }
        public string Icerik { get; set; }
        public string ResimYolu { get; set; }
    }

Feel free to modify the example to fit your needs.  Remember to use the debugging tools and make at least an attempt to troubleshoot.