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The phrase "a population of only" is correct and usable in written English.
It can be used when discussing the size or characteristics of a specific group or population, often to emphasize its smallness or limited nature.
Example: "The study focused on a population of only 50 participants, which may affect the reliability of the results."
Alternatives: "a mere population of" or "a population consisting of just".
Exact(60)
Hong Kong, with a population of only six million, has roughly the same number.
With a population of only 50,000, there are more sheep than people.
The town, with a population of only 3,000 people, has three Bach choirs.
With a population of only 18 million, Australian home-movie pickings can be mixed.
Amherst County, with a population of only 22,953, is not given any independent representation in the Virginia House.
Not bad for a place with a population of only 6 million.
A population of only about 6,000 remains in fragments of habitat.
Western Australia is larger than the whole of western Europe, but has a population of only around 2.5 million.
That tiny, volatile sliver of a state, wedged between Syria and Israel, has a population of only four million.
As recently as 1980, it had a population of only 20,000.
He estimated the crowd at 30,000, in a town with a population of only 2,000.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com