Only a few people with faimily name Zaja live in Croatia today, in households. There were 10 of them in the middle of the past century, and their number remains constant. They are located in one Croatian city only, in Trogir (<5).
In the sources analysed in the project Acta Croatica so far, the name is mentioned over ten times, the first time 2007 in source Encyclopaedia of Croatian Surnames.