The correct spelling of the word is "ostracize" (/ˈɑːstrəsaɪz/), not "ostracite". The word derives from the Greek "ostrakon", meaning "potsherd, tile". In Ancient Greece, citizens would vote by writing the name of a person they wanted to exile on a shard of pottery, which was called an ostrakon. The correct spelling has a "z" at the end, not an "s", and is pronounced with the stress on the second syllable.
A term applied to any fossil oyster.
Etymological and pronouncing dictionary of the English language. By Stormonth, James, Phelp, P. H. Published 1874.