Recently, the superconducting properties of Fibonacci quasicrystals have attracted considerable attention. By numerically solving the self-consistent Bogoliubov-de Gennes equations for an $s$-wave superconducting Fibonacci chain, we find that the system exhibits universal end superconductivity, where the pair potential at the chain ends can persist at higher temperatures compared to the bulk critical temperature ($T_{cb}$) of the condensate in the chain center. Furthermore, our study reveals two distinct critical temperatures at the left ($T_{cL}$) and right ($T_{cR}$) ends of the chain. This complex behavior arises from the competition between topological bound states and critical states, a characteristic of quasicrystals. With the chosen parameters, the maximal enhancement of $T_{cR}$ reaches up to $66\%$ relative to $T_{cb}$, while $T_{cL}$ can increase by up to $31\%$. Our study sheds light on the phenomenon of end superconductivity in Fibonacci quasicrystals, pointing to alternative pathways for increasing the superconducting critical temperature.

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• Superconducting order parameter
• Superconductivity
• Transition temperature
• Quasicrystals
• Bogoliubov-de Gennes equations