SELECT 
  category_id, 
  parent_id 
FROM 
  cscart_categories 
WHERE 
  parent_id IN(20163) 
  AND category_id != 1

Query time 0.00004

JSON explain

{
  "query_block": {
    "select_id": 1,
    "nested_loop": [
      {
        "table": {
          "table_name": "cscart_categories",
          "access_type": "ref",
          "possible_keys": ["PRIMARY", "parent", "p_category_id"],
          "key": "parent",
          "key_length": "3",
          "used_key_parts": ["parent_id"],
          "ref": ["const"],
          "rows": 20,
          "filtered": 100,
          "attached_condition": "cscart_categories.category_id <> 1"
        }
      }
    ]
  }
}

Result

category_id parent_id
20164 20163
20196 20163
20328 20163
20334 20163
20347 20163
20358 20163
20388 20163
20428 20163
20554 20163
20944 20163
21116 20163
21122 20163
21148 20163
21149 20163
21161 20163
21188 20163
21196 20163
21197 20163
21091 20163
20186 20163