What is the expiation (fidya) due from someone who promised God not to commit a sin but then committed it, and is it permissible for someone who is unemployed to take the cost of the expiation from his father?

A Muslim must avoid sins, both apparent and hidden. A mere promise is not an oath, but it must be fulfilled because abandoning sin is inherently obligatory, and this obligation is further confirmed by the promise made to Allah. Failure to fulfill a promise is one of the signs of hypocrisy, as the Prophet, peace and blessings be upon him, said: "The signs of a hypocrite are three: when he speaks, he lies; when he promises, he breaks his promise; and when he is entrusted, he betrays." Fulfilling a promise made to Allah is even more important. What is incumbent upon you is to repent to Allah for committing the sin and breaking your promise; there is no expiation required of you other than that.