Abstract We report on the formation of a large magnetic coherent structure in a vortex expansion-contraction interval, resulting from the merger of two plasmoids driven by a supergranular vortex observed by Hinode in the quiet-Sun. Strong vortical flows at the interior of vortex boundary are detected by the localized regions of high values of the Instantaneous Vorticity Deviation, and intense current sheets in the merging plasmoids are detected by the localized regions of high values of the Local Current Deviation. The spatiotemporal evolution of the line-of-sight magnetic field, the horizontal electric current density, and the horizontal electromagnetic energy flux is investigated by elucidating the relation between velocity and magnetic fields in the photospheric plasma turbulence. A local and continuous amplification of magnetic field from 286 G to 591 G is detected at the centre of one merging plasmoid during the vortex expansion-contraction interval of 60 min. During the period of vortex contraction of 22.5 min, the line-of-sight magnetic field at the centre of plasmoid-1 (2) exhibits a steady decrease (increase), respectively, indicating a steady transfer of magnetic flux from plasmoid-1 to plasmoid-2. At the end of the vortex expansion-contraction interval, the two merging plasmoids reach an equipartition of electromagnetic energy flux leading to the formation of an elongated magnetic coherent structure encircled by a shell of intense current sheets. Evidence of the disruption of a thin current sheet at the turbulent interface boundary layers of two merging plasmoids is presented.