SELECT 
  category_id, 
  parent_id 
FROM 
  cscart_categories 
WHERE 
  parent_id IN(
    18597, 18598, 18599, 18600, 18601, 18602, 
    18603, 18604, 18605, 18606, 18607, 
    18608, 18609, 18610, 18611, 18612, 
    18616, 18617, 18618, 18619
  ) 
  AND category_id != 1

Query time 0.00022

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": 22,
          "filtered": 100,
          "index_condition": "cscart_categories.parent_id in (18597,18598,18599,18600,18601,18602,18603,18604,18605,18606,18607,18608,18609,18610,18611,18612,18616,18617,18618,18619)",
          "attached_condition": "cscart_categories.category_id <> 1"
        }
      }
    ]
  }
}