"sit in jail" is a correct and usable expression in written English. You can use it to refer to someone being incarcerated in a jail or prison. زندانی شدن/به زندان افتادن/حبس کشیدن/در زندان به سر بردن/ آب خنک خوردن/
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مثال:
He was sentenced to three years in prison and had to sit in jail during this time.
او به سه سال زندان محکوم شد و چاره ای جز کشیدن این مدت از حبس نداشت.