Microfluidic systems have been widely used in various in vitro tissue engineering models. In this paper, we present a new microfluidic system for manufacturing cell filaments laden with cell aggregates of various shapes (beads, rosaries, and filaments) in the core region. The structures were obtained using the Rayleigh-Plateau instability of the two-phase flow of the injected bioinks (continuous phase of collagen/poly[ethylene glycol] diacrylate [PEGDA] and a dispersed phase of methacrylated gelatin (GelMA)). To demonstrate the potential of the system at the neuromuscular junction in vitro model, we injected a C2C12-laden collagen/PEGDA bioink into the sheath region and GelMA mixed with motor neuron cells (NSC-34) into the core region of the fabricated cell aggregates. The rosary-shaped NSC-34 aggregate in the core exhibited higher cell viability and more developed neurogenic gene expression than the cell aggregates of beads and filaments in the core region, owing to much greater mechanotransduction. Furthermore, when comparing the cell-laden struts (C2C12 in the sheath region and NSC34 in the rosary core region) with normally bioprinted struts with the same cell density, the expressions of myogenesis-, neuromuscular junction (NMJ)-, and neurogenesis-related genes in struts laden with rosary-shaped cell aggregates were significantly upregulated. The results of these experiments demonstrate the potential for the fabrication of new cell-laden core-sheath structures, which could be used for designing various in vitro models.