If I bring only part of the earnings into Turkey, does the deduction apply to that part?

No. The condition is that all of the earnings are transferred to Turkey by the date the annual return is due. If only part is brought in, the deduction is lost entirely, including for the part that was brought in. A transfer made after the deadline does not restore the deduction in later periods either. For income taxpayers the date is the end of March; for companies using the calendar year as their accounting period, the end of April.