How should a girl who has recently reached puberty and whose menstrual cycle is disturbed and irregular—in terms of duration and date of period—act in the month of Ramadan to avoid sin?

The maximum duration of menstruation according to the majority of scholars is 15 days and nights. So, if the total duration of blood your daughter experiences—including the period of purity (ṭuhr) interspersed within it—is 15 days or less, all of that is considered menstruation (ḥayḍ). She must perform ghusl (ritual bath) when she sees purity, and then pray and fast. Then, if she sees blood again, she returns to the state of being menstruating as long as the total duration does not exceed 15 days.

However, if the duration of her bleeding and the intermitted cessation exceeds 15 days and nights, she is considered to have istihāḍah (non-menstrual vaginal bleeding). If she has a valid distinction (tamyīz), she should consider the blood she counts as menstruation—which is the black, thick, and odorous blood—and anything other than that is istihāḍah. In this case, she performs ghusl once after the end of her menstrual period, then prays, fasts, and performs ablution (wuḍūʾ) for each prayer.

If she does not have a distinction (mumayyiza) and has no previous habit because she is a beginner (mubtadaʾa), she should consider herself menstruating for six or seven days, which is the common habit of women among her relatives. After that, she performs ghusl, and her ruling thereafter is that of a woman with istihāḍah.