What is the Islamic ruqyah or the Qur'anic verses that can be recited to stop my mother's continuous menstrual bleeding, which has not ceased for a month and a half?

What your mother experienced, the prolonged bleeding, is istihadah (non-menstrual vaginal bleeding) and not menses. She should stop praying and fasting for the duration of her menstrual period. This period is determined either by distinguishing the menstrual blood, or by referring to her known habitual period. If she cannot distinguish the blood and has no regular habit, her menses are considered to be six or seven days, as mentioned in the hadith. Whatever exceeds that is istihadah blood, which does not prevent her from praying and similar acts of worship. She must purify herself and pray for each obligatory prayer, and she is permitted to combine two prayers. As for treatment, it can be through ruqyah (Islamic exorcism) and supplication, or through medical treatment with doctors.