SELECT 
  category_id, 
  parent_id 
FROM 
  q_categories 
WHERE 
  parent_id IN(352)

Query time 0.00021

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "4.80"
    },
    "table": {
      "table_name": "q_categories",
      "access_type": "ref",
      "possible_keys": [
        "parent"
      ],
      "key": "parent",
      "used_key_parts": [
        "parent_id"
      ],
      "key_length": "3",
      "ref": [
        "const"
      ],
      "rows_examined_per_scan": 4,
      "rows_produced_per_join": 4,
      "filtered": "100.00",
      "cost_info": {
        "read_cost": "4.00",
        "eval_cost": "0.80",
        "prefix_cost": "4.80",
        "data_read_per_join": "10K"
      },
      "used_columns": [
        "category_id",
        "parent_id"
      ]
    }
  }
}