Serbian Greek-Catholics are of the Apostolic Exarchate of Serbia and Montenegro, a canonical jurisdiction erected in 2003 from territory formerly of the Eparchy of Krizevci of the Croats. Although, like all apostolic exarchates, it is immediately subject to the Oriental Congregation, the exarchate is deemed to be a jurisdiction of the Croatian Greek-Catholic Church and is reported as such in the
Annuario Pontificio.
The exarchate had 21 parishes, about as many priests, and 65 female religious, serving some 23,000 faithful, according to the most recent edition of the AP. The incumbent exarch is Kyr Djura (Dzudzar). You can read a 2006 interview with him
here.
The majority of the faithful are Montenegrons or persons of Carpatho-Rusyn or Ukrainian heritage; the number of ethnic Serbian Greek-Catholics would be very small (most ethinic Serbian Catholics are of the Latin Church). The vast majority of Serbians are Orthodox.
There are no Serbian Greek-Catholic parishes in the diaspora. In the US, immigrant faithful from Serbia would be committed to the pastoral care of the Byzantine (Ruthenian) Metropolia, as are the faithful of the parent Croat Greek-Catholic Church. (There is a single Croat GC parish extant in the Eparchy of Parma of the Ruthenians - St Nicholas the Wonderworker Croatian Greek-Catholic Church in Cleveland.)