SELECT 
  category_id, 
  parent_id 
FROM 
  cscart_categories 
WHERE 
  parent_id IN(
    7278, 7272, 7274, 7270, 7268, 7238, 7352
  ) 
  AND category_id != 1

Query time 0.00059

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "5.66"
    },
    "table": {
      "table_name": "cscart_categories",
      "access_type": "range",
      "possible_keys": [
        "PRIMARY",
        "parent",
        "p_category_id"
      ],
      "key": "parent",
      "used_key_parts": [
        "parent_id",
        "category_id"
      ],
      "key_length": "6",
      "rows_examined_per_scan": 27,
      "rows_produced_per_join": 27,
      "filtered": "100.00",
      "using_index": true,
      "cost_info": {
        "read_cost": "2.96",
        "eval_cost": "2.70",
        "prefix_cost": "5.66",
        "data_read_per_join": "70K"
      },
      "used_columns": [
        "category_id",
        "parent_id"
      ],
      "attached_condition": "((`nuie_scalesta_net`.`cscart_categories`.`parent_id` in (7278,7272,7274,7270,7268,7238,7352)) and (`nuie_scalesta_net`.`cscart_categories`.`category_id` <> 1))"
    }
  }
}