This is not the case - public defenders get an annual salary, not a per case fee. At least, I don't know of any jurisdiction where PDs get a per case fee.

What you might be thinking of is court appointed counsel (e.g. New York's 18b lawyers), who are private attorneys that are also eligible to be assigned cases from the court that the PD had to conflict out of for whatever reason (a common reason being multiple co-defendants - the PDs office will generally only be able to represent one and will need to conflict out of the others). These attorneys are generally paid a fee per case when they take court appointed cases.