Self generated magnetic field by an amplitude modulated intense laser beam in a tunnel ionized inhomogeneous plasma embedded with atomic clusters is studied. The transverse profile of the laser (along $$ {\hat{{y}}}$$ y ˆ ) is cosine and the clusters are taken to undergo Coulomb explosion thereby creating a plasma with decreasing density with time. The laser exerts a ponderomotive force $$ {\vec{{F}}}_{{p}} $$ F → p on the electrons, imparting them a transverse velocity $$ {\vec{{v}}} $$ v → . The current density $$ {\vec{{J}}} $$ J → , thus produced is irrotational i.e. $$ \nabla \times {\vec{{J}}}\,\, \ne \,\, 0 $$ ∇ × J → ≠ 0 , and gives rise to a quasistatic magnetic field along $$ {\vec{{F}}}_{{p}} \, \times \,\nabla \,{{n}}_{ 0} $$ F → p × ∇ n 0 . The generated magnetic field amplitude is sensitive to electron plasma frequency and laser modulation frequency. The peak value of generated magnetic field at resonance is ~40 MGauss at laser intensity 1015 W/cm2.