Is it permissible to fast on Friday or Saturday as a punishment for not performing the Fajr prayer, knowing that the intention of fasting is not for the virtue of the day but for the negligence of the Fajr prayer?

If the aforementioned covenant is a vow or indicative of one, then it is a vow of obstinacy (Nathr Lajaj), and the rulings mentioned in Fatwa no. 46162 apply to it. However, if it was merely a thought, then it is not a vow. There is no harm in fasting on Friday or Saturday if it coincides with a vow or a compensatory fast (qada'). If you missed the Fajr prayer and decided to fulfill the vow, which is fasting, then you must fast on another day due to missing the intention at night (tabyeet al-niyyah), and it is obligatory upon you to observe the Fajr prayer in congregation.