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To add a childs paternal father to a birth certificate a dna test will have to be done and a court order that such tests proves that the deceased father his the paternal father will have to be issued. If he is the paternal father you can not prevent his name from being added to the birth certificate if they can prove paternity (however you may be able to make a claim on his estate for child support etc. if that is a route you wish to go down).
If the other side has had a dna test done on the child you will need to see the proof and may want to have your own done to confirm.
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