See if searching for it with the last name of his mother (maiden name) instead of the last name of his father.
Some states will not put the father’s last name on unless they are married. Maybe they even have to show a marriage certificate which they don’t have with them so the baby is misnamed. Maybe his mother was still using her maiden name and the person who filled out the form was confused.
Who knows, it may work.
Also, there is an online service many states use that might help.
Also, if he thinks he was born in one place because that’s where they were living when he was born, try looking in the place where his maternal grandparents lived, or if his parents moved shortly before his birth, where they used to live.
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All the above is based on the idea his parents are no longer alive. If they are alive, ask them.