The emergence of charge-neutral fermionic excitations in magnetic systems is one of the unresolved issues in recent condensed matter physics. This type of excitations has been observed in various systems, such as low-dimensional quantum spin liquids, Kondo insulators, and antiferromagnetic insulators. Here, we report the presence of a pronounced gapless spin excitation in the low-temperature antiferromagnetic state of YbCuS2 semiconductor, where trivalent ytterbium atoms form a zigzag chain structure. We confirm the presence of this gapless excitations by a combination of experimental probes, namely 63/65Cu-nuclear magnetic resonance and nuclear quadrupole resonance, as well as specific heat measurements, revealing a linear low-temperature behavior of both the nuclear spin-lattice relaxation rate 1/T1 and the specific heat. This system provides a platform to investigate the origin of gapless excitations in spin chains and the relationship between emergent fermionic excitations and frustration.