The formation and the dynamics of coherent magnetic field structures in the context of laser plasma interaction has attracted considerable attention. In the literature the formation of these structures has, however, mostly been reported in the wake of a laser pulse propagating in an underdense plasma medium (Bulanov et al., Phys. Rev. Lett., vol. 76, 1996, pp. 3562–3565; Nakamura & Mima Phys. Rev. Lett., vol. 100, 2008, 205006; Bulanov et al., Plasma Phys. Rep., vol. 31, no. 5, 2005, pp. 369–381; Naumova et al., Phys. Plasmas, vol. 8, no. 9, 2001, pp. 4149–4155; Nakamura et al., Phys. Rev. Lett., vol. 105, no. 13, 2010, 135002). The study here focuses on the formation of coherent structures by an intense laser pulse when it interacts with an overdense plasma medium. The laser in this case gets reflected and partially dumps its energy to the lighter electrons species. Particle-in-cell simulation studies have been carried out in two dimensions to show that the energetic electrons (generated at the critical layer and having relativistic energies), together with the background plasma electrons often self-organize to form distinct electron current vortices. These electron vortices have associated magnetic fields with monopolar or dipolar symmetries depending on the rotation profile of the electron current. The formation, stability and dynamics of these structures in the context of overdense plasma is of special importance as they provide a possibility of energy transport into those regions of plasma which are inaccessible to lasers. For such applications, higher energy content (involvement of relativistic electrons in their formation) of these structures is desirable. It is shown that their salient propagation characteristics even at relativistic energies follow the rules of electron magnetohydrodynamics (EMHD) (Isichenko & Marnachev, Sov. Phys. JETP, vol. 66, 1987, p. 702; Biskamp et al., Phys. Rev. Lett., vol. 76, 1996, p. 1264) (Generalized - EMHD Yadav et al., Phys. Plasmas, vol. 15, no. 6, 2008, 062308; Yadav et al., Phys. Plasmas, vol. 16, no. 4, 2009, 040701) for homogeneous (inhomogeneous) plasma medium, respectively.