Half the cost of what?
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I don't know what he paid half of. if he paid expenses for your daughter, he did it voluntarily. Unless he has proof that the money was intended as a loan, he has no right to repayment. If the child is also his daughter, he has an obligation to support her.
If he is talking about household expenses, the same rule applies. He needs proof that the money was a loan and that there was an agreement that you would repay him.
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