Only in the moment which static electricity is discharged because magnetic fields are ~ dI/dt. read more
Static electric fields do not interact with static magnetic fields. This is why these two fields were considered unrelated phenomena in the early 1800's, until Faraday discovered the appearance of an electric field when a magnetic field changes in time. read more
If you really believe that the magnetic field is some magical, independent entity that has to be tested in every conceivable configuration, then sure, it's possible that a static charge (or a flux capacitor or a unicorn) will produce a magnetic field. read more