Military service record of the Austra-Hungary Empire are available to be researched in several archives - in Austria, in Hungary, in Croatia and in Serbia, both in historical and in military archives.

Check what is available via LDS on microfilms too.

You will need to figure out which regiment he was in or at least the wider military district command of the territory he was recruited from to narrow it down to records you need.

There are some military death records available for WWI in the Croatia vital records collection that is online via familysearch, but these are so mixed up you would need to comb them all name by name to see if he is in them :

https://familysearch.org/search/image/index#uri=https%3A%2F%...

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"Rodoslovlje" Serbian Genealogy Society
www.rodoslovlje.com