Is it obligatory for me to maintain ties with my father who accused me of being a child of fornication, accused my mother of fornication, and disowned me?

Denying and disavowing one's child is a serious matter. Whoever disavows their child, Allah will veil Himself from them and expose them. If a father denies the lineage of his child and accuses the mother of adultery without proof, he has committed a grave sin and slander. Lineage cannot be denied except through li'an (oath of condemnation) after the birth or immediately upon becoming aware of it. Whoever remains silent after that is not permitted to deny the lineage, and this is the view of the majority of scholars. The fundamental principle is that he is your father, and you must honor him, treat him kindly, maintain ties with him, and beware of disobeying him. Shunning him is not permissible according to Islamic law. As for disliking him in your heart, there is no sin in it as long as it is involuntary.