Barry didn’t write a damned thing as editor of the Review. No one who was there recalls seeing anything.
Respectfully, it's believed Obama wrote the unsigned six-page note at 103 Harv. Law Rev. 823 (1990).
Law Reviews have signed articles and unsigned notes. It's unheard of for a Law Review editor not to have a signed article. Obama didn't.
However, it's thought he wrote the note on whether unborn children have a right to sue a mother for potential damage due to drug use, etc. Obama reasoned they couldn't due to Roe v. Wade and an Illinois Supreme Court case, among other arguments. It was a pie-in-the-sky article - theoretical and not practical law. Something that just required being pompous and not a lot of research; certainly nothing that could be attacked on academic grounds.