  We compute the real-space profile of the superconducting order parameter (OP)
in a hybrid ring that consists of a 1D superconductor connected to a Fibonacci
chain using a self-consistent approach. In our study, the strength of the
penetration, as measured by the order parameter at the center of the
quasicrystal, depends on the structural parameter $\phi$, or phason angle, that
characterizes different realizations of the Fibonacci chains of a given length.
We show that the penetration strength dependence on $\phi$ reflects properties
of the topological edge states of the Fibonacci chain. We show that the induced
superconducting order parameter averaged over all chains has a power law decay
as a function of distance from the S-N interface. More interestingly, we show
that there are large OP fluctuations for individual chains and that the
penetration strength in a finite Fibonacci chain can be significantly $larger$
than in a normal periodic conductor for special values of $\phi$.
