  High critical temperature superconductivity often occurs in systems where an
antiferromagnetic order is brought near $T=0K$ by slightly modifying pressure
or doping. CaKFe$_4$As$_4$ is a superconducting, stoichiometric iron pnictide
compound showing optimal superconducting critical temperature with $T_c$ as
large as $38$ K. Doping with Ni induces a decrease in $T_c$ and the onset of
spin-vortex antiferromagnetic order, which consists of spins pointing inwards
to or outwards from alternating As sites on the diagonals of the in-plane
square Fe lattice. Here we study the band structure of
CaK(Fe$_{0.95}$Ni$_{0.05}$)$_4$As$_4$ (T$_c$ = 10 K, T$_N$ = 50 K) using
quasiparticle interference with a Scanning Tunneling Microscope (STM) and show
that the spin-vortex order induces a Fermi surface reconstruction and a
fourfold superconducting gap anisotropy.
