Self-assembled nanoscale channels may naturally arise in the growth process of grain boundaries (GBs) in high critical temperature superconductor (HTS) systems, and deeply influence the transport properties of the GB Josephson junctions (JJs). By isolating nano-channels in YBCO biepitaxial JJs and studying their properties, we sort out specific fingerprints of the mesoscopic nature of the contacts. The size of the channels combined to the characteristic properties of HTS favors a special regime of the proximity effect, where normal state coherence prevails on the superconducting coherence in the barrier region. Resistance oscillations from the current–voltage characteristic encode mesoscopic information on the junction and more specifically on the minigap induced in the barrier. Thouless energy emerges as a characteristic energy of these types of Josephson junctions. Possible implications on the understanding of coherent transport of quasiparticles in HTS and of the dissipation mechanisms are discussed, along with elements to take into account when designing HTS nanostructures.