Can You Engage in Foreplay while Fasting?
Question

I engaged in foreplay with my wife during the day in Ramadan – when we were both fasting – until I ejaculated semen. Allah knows best whether she also reached climax or not. But I feel very guilty and my heart is filled with pain because I feel that we have committed a great sin.
 Is there really any burden of sin on us? If so, what is the kaffarah (expiation)?.
Praise be to Allah.Engaging with wife while fasting until ejaculation
You committed a sin by engaging in foreplay with your wife until you ejaculated, because by doing so you invalidated your fast and violated the sanctity of this blessed month, and you missed out on the reward of fasting, concerning which Allah says: “He gives up his desire and his food for My sake.” (Narrated by al-Bukhari, 1761)
Your regret for the action that you did is repentance. The Prophet (peace and blessings of Allah be upon him) said: “Regret is repentance.” (Narrated by Ahmad, 3558; Ibn Majah, 4252; classed as sahih by al-Albani in Sahih Ibn Majah, 3429)
By ejaculating you broke your fast on the day when that happened, but you should refrain from eating and drinking for the rest of the day, until sunset. And you have to fast another day to make up for that day.
Expiation for intercourse while fasting
With regard to the kaffarah (expiation) , if you had had intercourse with your wife, the expiation would have been severe, namely freeing a slave. If you could not do that, then you would have to fast for two consecutive months. And if you could not do that, then you would have to feed sixty poor persons. 
 But if you ejaculated without having intercourse , then you do not have to offer expiation, rather you only have to make up that day.
 Al-Nawawi (may Allah have mercy on him) said:
“If he kisses his wife or has intimacy without penetration , or touches the hand of a woman with his hand etc, then he ejaculates, he has broken his fast. Otherwise (his fast is not broken).” (Al-Majmu’, 6/322)
 Shaykh Muhammad ibn ‘Uthaymin (may Allah have mercy on him) said:
“If (a man) touches his wife, whether he touches her with his hand, or with his face by kissing her, or with his private part (without having intercourse), then if he ejaculates he has broken his fast, but if he does not ejaculate then he does not break his fast thereby.” (Al-Sharh al-Mumti’, 6/388)
This ruling applies both to you and to your wife. If she reached climax as a result of this foreplay then she also broke her fast, and she has to repent to Allah and make up for this fast on another day. If she did not reach climax then she does not have to do anything.
For more, please see these answers: 38287 , 1051 , 279524 , 37679 , and 21806 .
And Allah knows best.