ogranak

1. (of an organization) branch; chapter
   Stranka je otvorila novi ogranak u Nišu. — The party opened a new branch in Niš.
   Radim u beogradskom ogranku jedne strane firme. — I work at the Belgrade branch of a foreign company.
2. (of mountains, rivers, families) offshoot; spur; branch
   Ovo brdo je ogranak Rudnika. — This hill is a spur of Mount Rudnik.
   Srpski spada u južnoslovenski ogranak slovenskih jezika. — Serbian belongs to the South Slavic branch of the Slavic languages.

For 'branch office', Serbia uses ogranak, filijala, ispostava; podružnica is also used, especially for branches of associations and organizations.