He engaged in foreplay with his wife during the night in Ramadan, then some maniy came out of him after the adhaan of Fajr

The fast is valid. The fact that semen came out afterthe adhaan of Fajr does notaffect the fast, because it is maniy that resultedfrom permissible intimacy (at a permissible time).

The scholars (may Allah have mercy on them) mentioneda similar matter, which has to do with one who has intercourse at night, then maniy comes out of him by day. They said: his fast isvalid.An-Nawawi (may Allah havemercy on him) said: If he has intercourse before Fajr,then withdraws when dawn breaks or immediately after dawn breaks, andejaculates, it does not invalidate his fast, because it resulted frompermissible intimacy, so nothing is required of him (by way of making up thefast).

End quote from al-Majmoo‘(6/350)

Muhammad ad-Dasooqi (mayAllah have mercy on him) said: If he has intercourse at night, and emits semenafter dawn, what appears to be the case is that nothing is required of him,like one who applies kohl at night then the kohl reaches his throat during theday.

End quote from Haashiyatal-Dasooqi (1/524).

And Allah knows best.