Short Story in the 50's - 60's, children from women around world impregnated by a cloud drifting in space.
Protagonist notes it's easier for him to stay hidden as his IQ is under 150. I want to find his quote.
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There are points of similarity to Children of the Atom, a fix-up novel by Wilmar H. Shiras. The first story, "In Hiding", is fairly well-known and has been in a lot of sf children themed anthologies. It was also in the Science Fiction Hall of Fame anthology.
The stories are about children around the world who are born super-intelligent, which fits with the OP's description. But, the root cause is radiation caused mutation (hence the name of the novel) instead of a space cloud, so that would be a vote against it. From Wikipedia
These children were born to workers caught in an explosion at an atomic weapons facility, and orphaned just a few months after birth when their parents succumbed to delayed effects from the blast.
The time frame is right, though.
This sounds a bit like The Midwich Cuckoos by John Wyndham, though that's not a short story, but a full novel.
The small English town of Midwich is caught in some sort of a stasis field for a day, after which all women are suddenly pregnant. They give birth to about 60 children, who are all blond and have psychic abilities.
Other towns and communities around the world have experienced the same, in Australia, Russia, Mongolia, and in the Arctic.
There is an elderly villager (I think ex-military) whom The Children, as they're called, trust. And while they're noted for their intelligence, I don't recall him or any other protagonist noting anything about his own IQ.
There's no cloud drifting in space, either.