Is it obligatory to fast while dark blood continues to flow after the third menstrual period, knowing that the child is six months old?

The maximum period for menstruation, according to the majority of scholars, is fifteen days. So, as long as the duration of the blood you are seeing has not reached fifteen days, you are still considered to be menstruating. Therefore, you must refrain from fasting and praying, and make up these days after Ramadan.