SELECT 
  a.category_id 
FROM 
  cscart_categories as a 
  LEFT JOIN cscart_categories as b ON b.category_id IN (313) 
WHERE 
  a.id_path LIKE CONCAT(b.id_path, '/%')

Query time 0.00021

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost": 0.060074355,
    "nested_loop": [
      {
        "table": {
          "table_name": "b",
          "access_type": "const",
          "possible_keys": ["PRIMARY", "p_category_id"],
          "key": "PRIMARY",
          "key_length": "3",
          "used_key_parts": ["category_id"],
          "ref": ["const"],
          "rows": 1,
          "filtered": 100
        }
      },
      {
        "table": {
          "table_name": "a",
          "access_type": "index",
          "key": "id_path",
          "key_length": "767",
          "used_key_parts": ["id_path"],
          "loops": 1,
          "rows": 271,
          "cost": 0.060074355,
          "filtered": 100,
          "attached_condition": "a.id_path like <cache>(concat('313','/%'))",
          "using_index": true
        }
      }
    ]
  }
}