kode html
 <div class="row">
       <div class="col-md-12">
           <label for="">Insert Keywords</label>
           <select name="search" id="" class="form-control select2"></select>
       </div>
 </div>

kode route
Route::get("/search", "TestingController@searchData")->name("search");

kode controller
public function searchData(Request $request)
    {
        $keywords = $request->get("search");
        if (!empty($keywords)) {
            $dataArray = array("1" => "Belajar", "2" => "select2", "3" => "ajax");
            return response()->json($dataArray, 200);
        }

    }

kode js
@push("script")
    <script type="text/javascript">
        $(function () {
            $('.select2').select2({
                theme: 'bootstrap4',
                minimumInputLength: 3,
                allowClear: true,
                placeholder: 'Keywords...',
                ajax: {
                    dataType: 'json',
                    url: '{{ route("search") }}',
                    delay: 800,
                    data: function (params) {
                        return {
                            search: params.term
                        }
                    },
                    processResults: function (data, page) {
                        console.log(data);
                        return {
                            results: data[0]
                        };
                    },
                }
            }).on('select2:select', function (evt) {
                var data = $(".select2 option:selected").text();
                alert("data selected : " + data);
            });
        });
    </script>
@endpush