Am I required to offer the expiation (kaffarah) of fasting three days for each day I failed to memorize the Quran, based on my oath to complete its memorization by the end of Ramadan at a rate of a quarter of a juz' as a maximum and one page as a minimum daily?

If a written oath is made with intention or utterance, it becomes binding, and expiation is due upon breaking it. If the oath specifies daily memorization, expiation is repeated with each instance of breaking it, unless the intention of the oath was for a daily average. Doubt concerning an oath does not necessitate expiation, as the default is the acquittal of responsibility. The expiation for an oath is feeding ten poor persons, or clothing them, or emancipating a slave. If none of these is possible, then it is fasting for three days.