Quantum entanglement is among the main fundamental resources for quantum information processing tasks like quantum communication, quantum computation, etc. The states with such kind of a nonlocal correlation can easily be obtained from a single-mode wave packet using a passive linear beam splitter. Taking into account scalable arguments and thus the need to implement quantum technologies in a solid-state platform, we study transmission of quantum data encoded in quasiparticles charges across a nanoscale three-arm beam splitter made by different BCS superconducting wires with a node size less than the smallest coherence length. It is calculated as to how a quasiparticle wave packet injected into one of the device leads is divided between two others. We show that an appropriate choice of the incoming wave packet permits to control the ratio of the two outgoing charges by comparatively small voltages of the order of the superconducting energy gap. The response of the device is analyzed as a function of the applied voltage biases and an asymmetry parameter, the ratio of the energy gaps in the two outward leads. We discuss two possible ways of the coherent wave-packet injection, specific pulses of voltages at ultra-low temperatures and those of current biases at temperatures comparable with the critical temperature of a superconducting emitter. Finally, we argue that voltages applied to outward leads as well as the temperature of an inward lead can serve as a control parameter for the charges delivered within a quantum network.