Is it permissible to fast on separate days to curb desire while not violating the Sunnah, and what is the ruling on singling out Saturday for fasting in this case?

There is no impediment to fasting any day voluntarily, except for the days that are prohibited from being singled out for fasting. Among these is Saturday, it is disliked to single it out for fasting unless it is an obligatory fast, or if the Muslim fasts a day before or after it, or if it coincides with someone's regular fasting. This is the view held by Ibn Qudamah, Al-Nawawi, and others, based on the Prophet's (peace be upon him) saying: "Do not fast on Saturday, except for what has been made obligatory upon you." The intent is to prevent a man from singling out Saturday for fasting in glorification of the Jews.