What is the Sharia ruling and the financial obligation towards an illegitimate son resulting from a previous relationship, after sincere repentance and attempts to find him?

The preponderant opinion is that the child born of adultery (zina) is not attributed to the adulterer, based on the Prophet’s (peace be upon him) saying: "The child is for the bed [of marriage]." Therefore, the child is not attributed to you in any way; rather, he is attributed to his mother. You are not bound by any material or non-material obligations towards him. You must renew your repentance and regret for what you have transgressed against Allah, and increase your seeking of forgiveness and performing expiating deeds such as prayer, fasting, and charity, for Allah Almighty says: "Indeed, good deeds do away with evil deeds."