What is the ruling on female students placing their books, which contain Quranic verses and the Basmala, under chairs or beside their feet?

Books containing the names of Allah, or His remembrance, or His verses, must be placed in suitable places, away from harm. This is part of revering Allah's شعائر (rituals/symbols) and حرمات (sacred things). Simply placing them in a bag is not considered desecration. One must avoid obsessive thoughts (waswas) and strive against oneself to get rid of them by disregarding them and paying them no mind, and by asking Allah for well-being.