Praise be to Allah.
Intercourse during the day in Ramadan
Intercourse during the day in Ramadan is haram for men and women alike, who are obliged to fast during the day. Doing that is a sin for which expiation (kaffarah) must be offered.
Expiation for having intercourse during Ramadan
The kaffarah is to free a slave; if that is not possible then the person must fast for two consecutive months; whoever is not able to do that must feed sixty poor persons.
Abu Hurayrah (may Allah be pleased with him) said: Whilst we were sitting with the Prophet (peace and blessings of Allah be upon him), a man came to him and said, “O Messenger of Allah, I am doomed!” He said, “What happened?” He said, “I had intercourse with my wife when I was fasting [in Ramadan].” The Messenger of Allah (peace and blessings of Allah be upon him) said, “Are you able to free a slave?” He said, “No.” He said, “Are you able to fast for two consecutive months?” He said, “No.” He said, “Can you feed sixty poor persons?'' He said, “No.” Then the Prophet (peace and blessings of Allah be upon him) remained silent for a while, and whilst we were like that, a large vessel of dates was brought to the Prophet (peace and blessings of Allah be upon him), and he said, “Where is the one who was asking?” He said, “Here I am.” He said, “Take these and give them in charity.” The man said, “Is there anyone more poor than me, O Messenger of Allah? For there is no household between the two harrahs (lava fields – i.e., in Madinah) that is poorer than my household.” The Messenger of Allah (peace and blessings of Allah be upon him) smiled until his eye teeth could be seen, then he said, “Feed it to your family.” (Narrated by al-Bukhari, 1834, 1835; Muslim, 1111)
Intercourse during the night in Ramadan
With regard to intercourse during the night in Ramadan, this is permitted and is not forbidden, and the time when it is permitted lasts until the onset of dawn. When dawn comes, intercourse becomes forbidden.
Allah says (interpretation of the meaning):
“It is made lawful for you to have sexual relations with your wives on the night of As-Sawm (the fasts). They are Libas [i.e. body-cover, or screen, or Sakan (i.e. you enjoy the pleasure of living with them] for you and you are the same for them. Allah knows that you used to deceive yourselves, so He turned to you (accepted your repentance) and forgave you. So now have sexual relations with them and seek that which Allah has ordained for you (offspring), and eat and drink until the white thread (light) of dawn appears to you distinct from the black thread (darkness of night), then complete your Sawm (fast) till the nightfall.” [al-Baqarah 2:187]
This verse clearly states that it is permissible to eat, drink and have intercourse during the nights of Ramadan until dawn.
After having intercourse it is obligatory to do ghusl, then pray Fajr.
And Allah knows best.