What is the expiation for touching a non-mahram woman with desire during the daytime in Ramadan while fasting?

The act committed by the questioner is a reprehensible deed that diminishes the reward of fasting, based on the Prophet's (peace be upon him) saying: "Whoever does not abandon false speech and acting upon it, Allah has no need for him to abandon his food and drink." Repentance erases sin, so if he repents with sincere repentance, it is hoped that Allah will forgive him. If nothing was emitted from him due to the act, then his fast is valid, and he does not need to make up for it. But if semen was emitted, then he must make up for that day due to the invalidation of his fast. If prostatic fluid (madhiy) was emitted, there is a difference of opinion regarding the invalidation of the fast, and the majority of scholars hold that it does not invalidate it.