Joseph J. Sullivan was a blackface comedian and acrobat in New York.
He is best known for composing the vaudeville song Where Did You Get That Hat?
It was a great success and he performed it many times thereafter.[1][2].
His other song compositions include Little Paddy Rooney in 1893.
Little else is known about his life, but in July 1922 a monthly New York theatre magazine described how he had recently 'brought back the "flannel-mouthed" Irish comedians when he regaled vaudeville patrons with Where Did You Get That Hat?'.