Does the emission of "madhy" after looking at an immodestly dressed girl necessitate making up a day of Ramadan, or a greater expiation?

The emission of pre-seminal fluid (madhy) does not invalidate the fast according to the majority of scholars. A Muslim must lower their gaze from what Allah has forbidden, as Allah Almighty says: "Tell the believing men to lower their gaze and guard their private parts. That is purer for them. Indeed, Allah is Acquainted with what they do," and as the Prophet, peace and blessings be upon him, said: "The glance is a poisoned arrow from the arrows of Iblees (Satan)."