Если вы хотите исключить дубликаты, используйте DISTINCT
:
SELECT
customerID,
SUM(payment) as totalpaid
FROM
(SELECT DISTINCT customerID, invoice, payment FROM customers)
GROUP BY customerID
Для customerID = 1
вы можете сделать
SELECT
customerID,
SUM(payment) as totalpaid
FROM
(SELECT DISTINCT customerID, invoice, payment FROM customers)
WHERE customerID = 1
без необходимости GROUP BY
.