Is it permissible to continue fasting upon the discharge of a few transparent, light red drops?

If drops appear after purification and before fifteen days have passed, they are not considered menstruation, and your fast is valid, based on the statement of Umm Atiyyah: "We did not consider brownish or yellowish discharge to be anything." However, if it occurs during the days of menstruation, then it is menstruation and one must break the fast.