SELECT 
  category_id, 
  parent_id 
FROM 
  cscart_categories 
WHERE 
  parent_id IN(
    4420, 4577, 4452, 4607, 8859, 4660, 4681, 
    4663, 4677, 4701, 4793, 5054, 5117, 
    8853, 5161, 8855, 8856, 4575, 4685, 
    4646, 4626, 8857, 8854, 4635, 4564, 
    4662, 4619, 4589, 4641, 4602, 4649, 
    4615, 9954
  )

Query time 0.00072

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "23.45"
    },
    "table": {
      "table_name": "cscart_categories",
      "access_type": "range",
      "possible_keys": [
        "parent"
      ],
      "key": "parent",
      "used_key_parts": [
        "parent_id"
      ],
      "key_length": "3",
      "rows_examined_per_scan": 56,
      "rows_produced_per_join": 56,
      "filtered": "100.00",
      "using_index": true,
      "cost_info": {
        "read_cost": "12.25",
        "eval_cost": "11.20",
        "prefix_cost": "23.45",
        "data_read_per_join": "332K"
      },
      "used_columns": [
        "category_id",
        "parent_id"
      ],
      "attached_condition": "(`webmarco`.`cscart_categories`.`parent_id` in (4420,4577,4452,4607,8859,4660,4681,4663,4677,4701,4793,5054,5117,8853,5161,8855,8856,4575,4685,4646,4626,8857,8854,4635,4564,4662,4619,4589,4641,4602,4649,4615,9954))"
    }
  }
}

Result

category_id parent_id
4575 4564
4626 4564
4635 4564
4660 4564
4681 4564
4701 4564
8859 4564
4589 4575
4602 4575
4615 4575
9647 4575
9954 4575
4619 4607
4641 4607
4649 4607
4646 4635
4793 4701
5054 4701
5117 4701
5161 4701
8855 4701
8856 4701
8857 4701
9657 4701
9659 4701
9662 4701
9655 5054
9656 5054
8853 5161
8854 5161
9672 8855