Praise be to Allah.
Yes, it is permissible for a person who is fasting to kiss his wife during the day in Ramadan, and for them to enjoy physical intimacy so long as it will not lead to intercourse or emission of maniy.
It was narrated that ‘Aa’ishah (may Allah be pleased with her) said: The Messenger of Allah (blessings and peace of Allah be upon him) used to kiss and touch (his wife) when he was fasting, but he was the most able of you to control his desire.
Narrated by al-Bukhaari (1927) and Muslim (1106)
What is meant by the words “but he was the most able of you to control his desire” is that he (blessings and peace of Allah be upon him) was able to control himself and to control his desire, so he would enjoy intimacy but that would not lead to intercourse or emission of maniy.
But if a man is afraid that if he kisses his wife whilst he is fasting, or enjoys intimacy with her, that this will lead to intercourse or emission of maniy, then he should refrain from that intimacy, so that he will not invalidate his fast.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: Kissing, with regard to one who is fasting, is divided into two categories: that which is permissible and that which is prohibited.
That which is prohibited is if he cannot be sure that he will not render his fast invalid.
That which is permissible is of two types:
1.where kissing will not provoke desire at all
2.where kissing may provoke desire, but he is confident that his fast will not be rendered invalid.
As for actions other than kissing that may lead to intercourse, such as embracing and the like, they come under the same ruling as kissing and there is no differentiation.
End quote from ash-Sharh al-Mumti‘ (6/429)
Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allah have mercy on him) was asked: If a man kisses his wife during the day in Ramadan, or touches her, does that invalidate his fast or not?
If a man kisses his wife, touches her and is intimate with her, without having intercourse, whilst he is fasting, all of that is permissible and there is nothing wrong with it, because the Prophet (blessings and peace of Allah be upon him) used to kiss his wife whilst he was fasting, and he used to touch her whilst he was fasting. But if he fears that he may end up doing that which Allah has prohibited to him, because he is easily aroused, then it is makrooh for him to do that. If he ejaculates, then he must refrain from eating and so on for the rest of the day, and he must make up that day’s fast, but he does not have to offer expiation, according to the majority of scholars.
End quote from Fataawa ash-Shaykh Ibn Baaz (15/315)
If a man kisses his wife whilst he is fasting and emits maniy, then he has invalidated his fast and he has to make up that day’s fast after Ramadan ends.
Ibn Qudaamah (may Allah have mercy on him) said: If the fasting person kisses his wife and ejaculates, then he has broken his fast, and there is no difference of scholarly opinion concerning that, as far as we know.
End quote from al-Mughni (4/361)
But he does not have to offer expiation, because expiation is only required if he breaks his fast by having intercourse. Please see fatwa no. 49750.
And Allah knows best.