Correct spelling for the English word "cajan" is [kˈad͡ʒən], [kˈadʒən], [k_ˈa_dʒ_ə_n] (IPA phonetic alphabet).
The word "cajan" is most likely a misspelling or variant spelling of the term "Cajun". The term Cajun refers to the French-speaking Acadian people who settled in the southern parts of Louisiana, particularly around the Acadiana region. The Acadians were originally French settlers in eastern Canada (present-day Nova Scotia, New Brunswick, and Prince Edward Island) who were forcibly removed by the British during the mid-18th century. They eventually found their way to Louisiana and became known as Cajuns. The word "Cajun" itself is believed to have derived from the term "Acadian", with its pronunciation possibly evolving over time due to language influences in the region, such as local Creole French and English.