What does the name Casitie mean?

As far as my knowledge spans, Casitie means nothing-- as it is a made-up name.

Having said that... I would imagine it to be a variant spelling of the name Cassidy.

Cassidy comes from an Irish surname which was derived from Ó Caiside, known to mean "Descendent of Caiside."

Consequently, Caiside is an Old Irish byname from the Ieish Gaelic cas; meaning "Curly Haired."