Is one's fast valid if a husband engages in foreplay with his wife, and semen is discharged from him three or four minutes after the adhan of Fajr?

Your fast is valid. The emission of semen after the dawn (Fajr) prayer call does not invalidate the fast, as it results from a permissible act of intimacy. Scholars have mentioned that if someone engages in sexual intercourse at night and semen is emitted during the day, their fast remains valid.