  Quasiperiodicity has long been known to be a potential platform to explore
exotic phenomena, realizing an intricate middle point between ordered solids
and disordered matter. In particular, quasiperiodic structures are promising
playgrounds to engineer critical wavefunctions, a powerful starting point to
engineer exotic correlated states. Here we show that systems hosting a
quasiperiodic modulation of antiferromagnetism and spin-singlet
superconductivity, as realized by atomic chains in twisted van der Waals
materials, host a localization-delocalization transition as a function of the
coupling strength. Associated with this transition, we demonstrate the
emergence of a robust quasiperiodic critical point for arbitrary incommensurate
potentials, that appears for generic relative weights of the spin-singlet
superconductivity and antiferromagnetism. We show that the inclusion of
residual electronic interactions leads to an emergent spin-triplet
superconducting state, that gets dramatically enhanced at the vicinity of the
quasiperiodic critical point. Our results put forward quasiperiodicity as a
powerful knob to engineer robust superconducting states, providing an
alternative pathway towards artificially designed unconventional
superconductors.
