  Fractal geometry presents us with a self-similarity in their pattern at
various length scales that is prevalent in our natural world. We present
theoretical model of a Sierpinski gasket (SPG) fractal geometry with a
deterministic perturbation in the form of a hierarchical distribution of
magnetic flux. Such flux configuration induces a deterministic disorder in the
Aharonov-Bohm (AB) phases picked up by the electron wavefunction. Using the
tight-binding formalism, we show that by tunning the strength of the hierarchy
parameter of those AB phases, one can systematically engineer quantum states in
a SPG fractal lattice. In addition to this, we have also observed that by
controlling the strength of this hierarchy parameter in the magnetic flux, one
can effectively regulate the persistent current in the SPG fractal structure.
This characteristic is found to be true for various filling factors. Our
results could be useful for designing nanoelectronic devices using molecular
fractal structures fabricated by chemical synthesis technique.
