SELECT 
  category_id, 
  parent_id 
FROM 
  cscart_categories 
WHERE 
  parent_id IN(
    7348, 7156, 7158, 7225, 7207, 7163, 7149, 
    7266, 7313
  ) 
  AND category_id != 1

Query time 0.00064

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "6.46"
    },
    "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": 31,
      "rows_produced_per_join": 31,
      "filtered": "100.00",
      "using_index": true,
      "cost_info": {
        "read_cost": "3.37",
        "eval_cost": "3.10",
        "prefix_cost": "6.47",
        "data_read_per_join": "80K"
      },
      "used_columns": [
        "category_id",
        "parent_id"
      ],
      "attached_condition": "((`nuie_scalesta_net`.`cscart_categories`.`parent_id` in (7348,7156,7158,7225,7207,7163,7149,7266,7313)) and (`nuie_scalesta_net`.`cscart_categories`.`category_id` <> 1))"
    }
  }
}