Is it permissible to continue supplicating to Allah for marriage to a specific person after contact has been severed with them, out of fear of Allah? And what should be done in this situation?

You did well to sever your relationship with this man, and you must not return to it. It is not permissible for a girl to establish a relationship with a non-mahram man. If he contacts you again, tell him firmly: "If you are sincere and want what is lawful, then approach homes through their doors and propose to me." Do not answer him again. These relationships are dangerous for a girl's future, especially online where lies and deception prevail. Marriage can be offered to him through one of your mahrams. Do not enter men's websites and forums, and put your trust in Allah concerning marriage.