What is the ruling on blood that accompanies white discharge outside the usual days of menstruation, and is it obligatory to make up for fasting and prayer during these days?

The drops seen by the questioner are not considered menstruation and do not necessitate making up for the fast, because the minimum duration of menstruation is one day and one night according to the majority of scholars. This was mentioned by Ibn al-Rif’ah al-Shafi’i, who based his reasoning on induction and narrated from Ali (may Allah be pleased with him) his saying: "The minimum duration of menstruation is one day and one night, and its maximum is fifteen days. Anything more than that is irregular bleeding (istihadah)."