SELECT 
  category_id, 
  parent_id 
FROM 
  cscart_categories 
WHERE 
  parent_id IN(
    18622, 18623, 18624, 18625, 18626, 18627, 
    18628, 18635, 18636, 18637, 18638, 
    18639, 18640
  ) 
  AND category_id != 1

Query time 0.00006

JSON explain

{
  "query_block": {
    "select_id": 1,
    "nested_loop": [
      {
        "table": {
          "table_name": "cscart_categories",
          "access_type": "range",
          "possible_keys": ["PRIMARY", "parent", "p_category_id"],
          "key": "parent",
          "key_length": "3",
          "used_key_parts": ["parent_id"],
          "rows": 18,
          "filtered": 100,
          "index_condition": "cscart_categories.parent_id in (18622,18623,18624,18625,18626,18627,18628,18635,18636,18637,18638,18639,18640)",
          "attached_condition": "cscart_categories.category_id <> 1"
        }
      }
    ]
  }
}