SELECT 
  cscart_product_prices.product_id, 
  MIN(
    IF(
      cscart_product_prices.percentage_discount = 0, 
      cscart_product_prices.price, 
      cscart_product_prices.price - (
        cscart_product_prices.price * cscart_product_prices.percentage_discount
      )/ 100
    )
  ) AS price 
FROM 
  cscart_product_prices 
WHERE 
  cscart_product_prices.product_id IN (
    3873, 3862, 262, 1785, 866, 3676, 3677, 
    323, 865, 864, 322, 324, 5071, 6426, 
    6428, 6429, 6427, 5615, 5613, 5614, 
    5611, 5612, 5692, 5693
  ) 
  AND cscart_product_prices.lower_limit = 1 
  AND cscart_product_prices.usergroup_id IN (0, 1) 
GROUP BY 
  cscart_product_prices.product_id

Query time 0.00055

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "16.81"
    },
    "grouping_operation": {
      "using_filesort": false,
      "table": {
        "table_name": "cscart_product_prices",
        "access_type": "range",
        "possible_keys": [
          "usergroup",
          "product_id",
          "lower_limit",
          "usergroup_id"
        ],
        "key": "product_id",
        "used_key_parts": [
          "product_id"
        ],
        "key_length": "3",
        "rows_examined_per_scan": 24,
        "rows_produced_per_join": 4,
        "filtered": "19.12",
        "index_condition": "(`dbggbern`.`cscart_product_prices`.`product_id` in (3873,3862,262,1785,866,3676,3677,323,865,864,322,324,5071,6426,6428,6429,6427,5615,5613,5614,5611,5612,5692,5693))",
        "cost_info": {
          "read_cost": "16.35",
          "eval_cost": "0.46",
          "prefix_cost": "16.81",
          "data_read_per_join": "110"
        },
        "used_columns": [
          "product_id",
          "price",
          "percentage_discount",
          "lower_limit",
          "usergroup_id"
        ],
        "attached_condition": "((`dbggbern`.`cscart_product_prices`.`lower_limit` = 1) and (`dbggbern`.`cscart_product_prices`.`usergroup_id` in (0,1)))"
      }
    }
  }
}

Result

product_id price
262 39.90000000
322 29.90000000
323 29.90000000
324 29.90000000
864 29.90000000
865 29.90000000
866 29.90000000
1785 169.90000000
3676 23.90000000
3677 23.90000000
3862 44.90000000
3873 44.90000000
5071 44.90000000
5611 34.90000000
5612 34.90000000
5613 34.90000000
5614 34.90000000
5615 34.90000000
5692 34.90000000
5693 34.90000000
6426 44.90000000
6427 44.90000000
6428 44.90000000
6429 44.90000000