What is the ruling on the fasting of one who purified herself from menstruation, then intermittent bleeding continued to issue from her throughout the month of Ramadan?

If the reality is as you described, then the drops of blood that appeared on you after purification from your regular period are not considered menstruation (hayd); because it is not continuous bleeding, it does not take the ruling of hayd. You are obligated to fast, pray, and perform ablution for the time of each prayer as long as it (the spotting) is present, like other women experiencing irregular bleeding (istihadah) and those with continuous discharge. Your fasting on those days is valid.