Is it permissible for a girl who has committed minor fornication (zina asghar) with a young man to refuse his marriage proposal out of fear of Allah's punishment, and is it permissible for the young man to propose to her with a sincere intention of repentance, and how can they be sure that their repentance is accepted, and what is the expiation or prescribed punishment for their act?

If "minor Zina" refers to the preliminaries of Zina, then you are obliged to make sincere repentance by cutting off your relationship with the girl. If you were engaged to her, then go to her guardian and complete the marriage if they agree; otherwise, seek another woman of good religious character and morals. The expiation for this act is sincere repentance and an increase in good deeds, for Allah Almighty says: "Indeed, good deeds do away with evil deeds." There is no prescribed punishment (hadd) for these actions; rather, they incur discretionary punishment (ta'zeer) from the ruler if he becomes aware of them. You should not inform anyone about what happened.