The informal celebratory day (October 16) is usually spelled
"Boss's Day", but can be "Bosses Day".
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Boss's day is the correct way to write it.
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Boss's Day was created in 1958.
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That is the correct spelling of Boss's Day, although in common use you can see Boss' Day, which is technically improper, and Bosses Day, and National Boss Day for the apostrophe-challenged.