David, thanks for your email. I do know that the surnames of BAIADA, BAIATA, BAJADA, BAJATA, are connected.
I was informed that in the mid 1600's the BAJADA's originated from Malta, and ended up in Palermo, Sicily.
I have been unable to trace beyond 1850's. The surnames you have are unfamiliar to me.
The other surnames connected by marriage to the BAIADA's are, Passalacqua, Gallina, and Mannino.
Regards from Melbourne, Australia.