Sometimes it was called a "calaboose".
I believe the word you are looking for is "hoosegow".
hoosegow was what I remember it being called.... probably called something different in each area of the country is my guess....
I also remember the expression being "in the clink" referred to being in jail. Then there was the "slammer". And the "big house". But in the old time Westerns it was usually hoosegow.
How about the Pokey?
oldwest jails called hoosecow
hoosegow, of course, is a corruption of juzgado.
"In the jug" also derives from juzgado.
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