SELECT 
  category_id, 
  parent_id 
FROM 
  cscart_categories 
WHERE 
  parent_id IN(
    3, 15, 2, 12, 16, 4, 13, 5, 10, 18, 20, 14, 
    17, 19
  ) 
  AND category_id != 1

Query time 0.00030

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "2.62"
    },
    "table": {
      "table_name": "cscart_categories",
      "access_type": "ALL",
      "possible_keys": [
        "PRIMARY",
        "parent",
        "p_category_id"
      ],
      "rows_examined_per_scan": 20,
      "rows_produced_per_join": 20,
      "filtered": "100.00",
      "cost_info": {
        "read_cost": "0.62",
        "eval_cost": "2.00",
        "prefix_cost": "2.62",
        "data_read_per_join": "53K"
      },
      "used_columns": [
        "category_id",
        "parent_id"
      ],
      "attached_condition": "((`betaatif_store`.`cscart_categories`.`parent_id` in (3,15,2,12,16,4,13,5,10,18,20,14,17,19)) and (`betaatif_store`.`cscart_categories`.`category_id` <> 1))"
    }
  }
}