Hi, I know next to nothing about parishes in Galicja, but since no one responded to your post, here is a handful of suggestions you might find useful.
The names you give in your message seem all to be distorted forms of the originals. I assume the place of birth is Dąbrowica. Unfortunatedly, even if that assumption is correct, there a quite a number of places with that name in today's Poland. Here is the list:
http://pl.wikipedia.org/wiki/D%C4%85browica
Three of them are located in what once was Galicja:
http://pl.wikipedia.org/wiki/D%C4%85bro ... 5%BCajski)
http://pl.wikipedia.org/wiki/D%C4%85bro ... %C5%84ski)
http://pl.wikipedia.org/wiki/D%C4%85bro ... nobrzeski)
To make things worse, there are two others in today's Ukraine in the region that once was Galicja, too:
http://pl.wikipedia.org/wiki/D%C4%85browica_(Ukraina)
http://pl.wikipedia.org/wiki/D%C4%85browica_(Ukraina)
The choice is yours.
The name of the parish – Sztezadi, does not sound Polish to me, not even Slavic; actually sounds more like Hungarian. The closest I could find is Szegdy:
http://pl.wikipedia.org/wiki/Szegdy
which actually is located close to one of the Dąbrowicas above. The problem with Szegdy is, however, that it seems to have never been a seat of a parish.
The surname Ignaz is almost certainly Ignac, which comes from the personal name Ignacy. Here is a map showing the distribution of people bearing that surname in today's Poland:
http://nazwiska-polskie.pl/Ignac
You will notice occurance of that surname close to one of the Dąbrowicas.
Here is my advice. There are a lot of people on this forum that are really knowledgeable about your region of interest. The key to success consists in locating the parish where the person you are looking for was baptized. Repost your message under different title, something like "Parish in former Galicja sought". For instance, I was unable to interpret the passage "Galizien u(nd) dorthin ztig [=zuständig]" from your post, but there will be others who can.
All the best with your search
and greetings from Poland
mlszw
