What is the ruling on the fast of a woman who purified herself at the beginning of Ramadan, then saw brown discharge and a little blood in its first days, then saw a little blood with white discharge in its last days, knowing that she takes pills to prevent menstruation?

The blood you saw on the fifth and sixth days of Ramadan (definition) is considered menstruation, and you are required to make up for the fasting of those two days. Your fasting on the first days is valid because the period of purity interspersed within menstruation is valid. What you saw on the twenty-third day, if it was little and did not amount to a day and a night, is not considered menstruation according to the majority of scholars, and your fasting is valid. However, making it up is more cautious, to avoid disagreement.