What is the ruling on fasting the days when bleeding occurred after treatment stopped and then resumed, knowing that these are makeup days and the intention to fast exists? Is the fast valid if it is after six days of purity?

The maximum duration of menstruation is fifteen days. If the blood, including any intervening periods of cleanness, exceeds this duration, or if blood reappears in less than thirteen days and cannot be combined with the previous bleeding to form a single menstrual period, then you are considered to have irregular bleeding (istihada). Therefore, if the bleeding occurs at a time when it is not valid to be menstruation, your fast is valid, and you must pray, perform ablution for each prayer, and take precautions.