What is the ruling on swearing an oath on the Qur’an while in a state of janabah, and does he owe expiation for breaking this oath?

We understand that your father ordered you to swear on the Qur'an that you would not resume correspondence with that girl or any other. It is your religious duty to sever that sinful relationship and to avoid falling into it by marrying, if able, or by fasting, if not. Your oath on the Qur'an is binding, and if you break it, you will incur expiation for breaking an oath, along with sin. If you touch the Qur'an while not in a state of ritual purity, you are sinful. You must obey your father and fulfill your oath by not returning to those things which are forbidden by Islamic law.