SELECT 
  category_id, 
  parent_id 
FROM 
  cscart_categories 
WHERE 
  parent_id IN(
    450, 424, 451, 452, 425, 426, 448, 449, 
    477, 492, 520, 585, 586, 657
  ) 
  AND category_id != 264

Query time 0.00082

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "11.16"
    },
    "table": {
      "table_name": "cscart_categories",
      "access_type": "range",
      "possible_keys": [
        "PRIMARY",
        "parent",
        "p_category_id"
      ],
      "key": "parent",
      "used_key_parts": [
        "parent_id"
      ],
      "key_length": "3",
      "rows_examined_per_scan": 17,
      "rows_produced_per_join": 17,
      "filtered": "100.00",
      "index_condition": "(`softwarepirmam_hewadelivard_cscart_4`.`cscart_categories`.`parent_id` in (450,424,451,452,425,426,448,449,477,492,520,585,586,657))",
      "cost_info": {
        "read_cost": "9.46",
        "eval_cost": "1.70",
        "prefix_cost": "11.16",
        "data_read_per_join": "53K"
      },
      "used_columns": [
        "category_id",
        "parent_id"
      ],
      "attached_condition": "(`softwarepirmam_hewadelivard_cscart_4`.`cscart_categories`.`category_id` <> 264)"
    }
  }
}

Result

category_id parent_id
450 424
451 424
452 424
426 424
492 424