would guess most for Landwehr-Infanterie or Gebirgstruppen, Gebirgsinfanterie:http://commons.wikimedia.org/wiki/File:GebInfanterieMa_n_7.p...http://de.wikipedia.org/wiki/K.k._Gebirgstruppehttp://www.militaria-lexikon.de/katalog/wk2/wk2_edelweiss/mi...
also looks for Zugsführer - Three six pointed white stars on the collar or collar patch:http://www.austro-hungarian-army.co.uk/badges/badges.htmhttp://de.wikipedia.org/wiki/Rangabzeichen_der_%C3%B6sterrei...http://www.austro-hungarian-army.co.uk/infunif.htm
where did he live (was born)? this maybe could help more.
and you can then ask in the present country now - so if they have still the files. need to know to get the direction we need. maybe also some other details would help to know WHERE to search for his military-service.