Is it obligatory to search for a father who abandoned his family and filed for divorce, in order to avoid cutting ties of kinship, or is it permissible to leave him?

Your father erred by neglecting and abandoning you without provision, thereby violating the Prophet's (PBUH) saying: "It is sufficient sin for a man to neglect those he is responsible to provide for." He has also betrayed the trust enjoined by Allah. However, despite this, it is not permissible for you to sever ties with your father. Rather, treat him well and maintain contact with him, because no matter what his condition, filial piety is an obligation and one of the greatest acts of closeness to Allah, especially in old age, as Allah Almighty says: "And your Lord has decreed that you worship none but Him, and to parents, good treatment. Whether one or both of them reach old age [while] with you, say not to them [uff] or repel them but speak to them a noble word." It is permissible to search for him to a moderate extent without hardship.