We have studied the electronic transport properties of open Sierpinski gasket systems connected to two electron reservoirs in the presence of a magnetic field. In the framework of a tight-binding model, the systems are composed of one-dimensional ordered chains. A generalized eigenfunction method, which allows one to deal with finite systems consisting of a large number of lattice sites (nodes), is used to calculate the transmission and reflection coefficients of the studied systems. The numerical results show that there are two kinds of symmetries of the transmission coefficient T to magnetic flux Phi, and there are antiresonant state regions (T = 0) and resonant states (T = 1). It is different from the open ring systems now the electronic energies of resonant states do not coincide with the eigenenergies of the isolated Sierpinski gasket systems. It is also found that the transmission behavior of the single exit systems is much more complicated than that of two exit systems. [S0163-1829(99)03640-1].