The interplay between real-space topology such as magnetic skyrmions and momentum-space topology characterized by topological surface states (TSSs) is predicted to realize novel phenomena and functionalities, yet materials hosting both topologies are scarce. Skyrmion-hosting helimagnet family EuGa₂Al₂ and EuAl₄ has been a prime candidate for such a dual-topology system, but conclusive evidence for its momentum-space topology has remained elusive. We provide this evidence by directly observing TSSs that stem from bulk Dirac nodal lines using high-resolution angle-resolved photoemission spectroscopy. These TSSs are exceptionally robust against various perturbations such as a 2×1 surface reconstruction, a chemical change in the termination of the crystal surface, and the onset of helical antiferromagnetic order. Crucially, below the Neel temperature, we observe replica bands driven by the magnetic ordering. Moreover, we demonstrate clear surface-termination dependence of this magneto-topological coupling. Our findings establish Eu(Ga₁₋ₓAlₓ)₄ as a dual-topology material and offer a rare platform to explore and control the interaction between the two fundamental topological realms.