No, your credit score will not suffer if you incur an overdraft fee. Overdraft protection, on the other hand, comes with its own set of repercussions.
If you regularly use overdraft protection and cannot pay it off in time, overdraft protection can indirectly impact your credit score.
In unpaid, the bank labels your account as “delinquent.” Banks then bring your account to the credit bureau, and your credit score will likely reflect this negative impact.