<select class="form-control" name="selected_sector2" id="category">
                            <option value="blank">Zgjedh sektorin</option>
                            @foreach($sektorat['sektorat2'] as $sektori2)
                            <option name="sektori">
                                {{ $sektori2->sektori_nr }}
                            </option>
                            @endforeach
                        </select>

                        <select class="form-control" id="subcategory" name="kuadratet">
                            <option value="blank">Zgjedh Kuadratin</option>
                        </select>

Route::get('shto/njesin-stratigrafike', 'NjesiteStratigrafikeController@shtoNjesiStratigrafike');

class NjesiteStratigrafikeController extends Controller
{
    public function shtoNjesiStratigrafike(){
        $selected_sector = Input::get('selected_sector2');
        $sector_id = Sektori::where('sektori_nr',$selected_sector)
                            ->value('sektori_id');

        $kuadratet = Kuadrati::where('sektori_id_fk', '=' ,$sector_id)->get();

        return Response::json($kuadratet);
    }
}

<script type="text/javascript">
          $('#category').on('change', function(e){

            var sektori_id = e.target.value;

               //ajax

               $.get('/shto/njesin-stratigrafike?sektori+id=' + sektori_id, function(data){

                   //success data
                   $('#subcategory').empty();

                   $('#subcategory').append(' Please choose one');

                   $.each(data, function(index, subcatObj){

                       $('#subcategory').append(''
                       + subcatObj.subcategory_name + '</option>');


                   });



               });
    });

    </script>