This sentence could be translated as "I'm living in Serbia". セルビア (Servia) に is the particle used to indicate location 住んでるんだ is the conjugation of the verb 住む (live) in the progressive form, in a more casual way, 住んでいる would be the more polite way of saying the same thing. Hope this helps (^^)

セルビアに住んでるんだね。means "You live in Serbia, don't you?" セルビア→Serbia　に　→in　　住んでる(住む)→(to live) だね→(~right?) same as "a tag question"

セルビア に 住んでる ん だ ね。 "Serbia" LOCATION "to live"-CONTINUATIVE INTERROGATIVE PARTICLE COPULA CONFIRMATION ("is that so?")