Magnetic fields are known to play a crucial role in the star formation process, particularly in the formation of jets and outflows from protostellar discs. The magnetic field structure in star forming regions is not always uniform and ordered, often containing regions of magnetic turbulence. We present grid-based, magneto-hydrodynamical simulations of the collapse of a 1 M cloud core, to investigate the influence of complex magnetic field structures on outflow formation, morphology and efficiency. We compare three cases: a uniform field, a partially turbulent field and a fully turbulent field, with the same magnetic energy in all three cases. We find that collimated jets are produced in the uniform-field case, driven by a magneto-centrifugal mechanism. Outflows also form in the partially turbulent case, although weaker and less collimated, with an asymmetric morphology. The outflows launched from the partially turbulent case carry the same amount of mass as the uniform-field case but at lower speeds, having only have 71% of the momentum of the uniform-field case. In the case of a fully turbulent field, we find no significant outflows at all. Moreover, the turbulent magnetic field initially reduces the accretion rate and later induces fragmentation of the disc, forming multiple protostars. We conclude that a uniform poloidal component of the magnetic field is necessary for the driving of jets.