What is the ruling on brown discharge that continues from after one menstrual period until the time of the next menstrual period, and when is ghusl (ritual bathing) required?

If the bleeding continues, along with the brown and yellow discharge, then you are experiencing istiḥāḍah (non-menstrual vaginal bleeding). If you have a regular menstrual cycle, observe it as your menses, and anything beyond that is istiḥāḍah. If you do not have a regular cycle, then apply the rule of discernment (tamīz): observe the bleeding and consider it menses if it is not less than one day and one night, and not more than fifteen days. If the bleeding stops and you see brown or yellow discharge, consider it istiḥāḍah. Once the period counted as menses has ended, you perform one ghusl (ritual bath), then perform wuḍūʾ (ablution) for each prayer after its time has begun. You pray the obligatory and supererogatory prayers with this wuḍūʾ until the time for that prayer exits. You must take precautions by tying a cloth over the area, as this yellow and brown discharge is impure.