What is the ruling on a daughter refusing to communicate with her father who denied her paternity and abandoned her?

No matter how great a father's injustice or dereliction of duty, it does not nullify his right to dutifulness and obedience in what is lawful. Allah has commanded us to accompany even polytheist parents with kindness, as He says: "But if they endeavor to make you associate with Me that of which you have no knowledge, do not obey them, but accompany them in [this] world with kindness." Therefore, the daughter must maintain ties with her father and obey him in what is lawful. Her mother should assist her in this and explain to her that her patience with her father's ingratitude, combined with her kindness towards him, is a path to earning Allah's pleasure, and that Allah does not waste the reward of those who do good, as He says: "Indeed, he who fears Allah and is patient, then indeed, Allah does not waste the reward of those who do good."