Does a daughter incur sin if she refrains from paying off her deceased father’s debts, knowing that she is able to pay them off, and that her father had disowned her at birth?

A father's negligence concerning his child's rights does not nullify his right to dutifulness and good companionship. However, your father's creditors cannot demand that you pay his debts from your private wealth, because a child is not obligated to pay his father's debt from his own money, nor is he sinful for not paying it, unless the father leaves behind an estate, from which the debt can then be paid.

Nevertheless, you should strive to pay your father's debt as an act of dutifulness and kindness, not out of obligation, to the best of your ability and capacity, in order to free him from the predicament of debt. This is based on the Prophet, peace and blessings be upon him, who said: "The soul of a believer is tied to his debt until it is paid off on his behalf."