A substantial fraction of high-atitude Fermi-LAT sources remain unidentified. These objects exhibit steady GeV emission, low variability, and no multiwavelength counterparts. We propose a phenomenological braneworld model in which accreting black holes on an adjacent brane trigger inter-brane wormholes, leaking hadronic gamma-ray and neutrino emission into our brane. The model provides a calculable chain from black-hole mass to integrated luminosity and differential spectra. A central methodological feature is that the source redshift z is treated as a free MCMC parameter with a unified prior log10(z) [belong to][-3.0,0.477] for all five competing models, eliminating circular flux—luminosity calibration. Fitting the 4FGL-DR4 high-atitude unassociated sample, the wormhole posterior peaks at z=0.066 (~290 Mpc), whereas dark matter and primordial black holes require unphysical local redshifts (z<0.05) and pulsar wind nebulae require z ~ 0.95. The model yields four distance-independent testable predictions: narrow variability, multiwavelength emptiness, a TeV spectral cutoff, and a coincident neutrino flux with F_nu / F_gamma ~ 0.5.