Is expiation obligatory for one who intentionally commits fornication and breaks their fast during the daytime in Ramadan, and what is the expiation if one is able to fast without disclosing the reason?

You must make up for the day you intentionally broke your fast and expiate for it by fasting for two consecutive months. Shyness from people is not an excuse to abandon expiation if you are able to fast. You can use dissimulation regarding the reason for your fast by stating that you vowed to fast for two months for the sake of Allah the Almighty.