It is assumed that it derived from the word baša, meaning "chief", itself a loanword from Turkish başı, meaning "head".
It is one of the most common surnames in two Dalmatian counties of Croatia.
[1] "In a blue background on a green ground, a warrior dressed in red with high black boots and a hat, left-handed sideways with gold with a belt to which black covers are fastened.
In his raised right he holds a scimitar with a golden cross opposite the neck of a kneeling bearded Turk dressed in a rainbow white kaftan with a belt, which with raised hands begs for mercy."
This description from the book is describing the conflicts that the Bassich family of Austria had against the Turks while defending Vienna.