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In this paper, we study the spin excitation properties of the frustrated triangular-lattice antiferromagnet $\mathrm{Yb}{({\mathrm{BaBO}}_{3})}_{3}$ with nuclear magnetic resonance. From the spectral analysis, neither magnetic ordering nor spin freezing is observed with temperature down to $T=0.26$ K, far below its Curie-Weiss temperature $|{\ensuremath{\theta}}_{w}|\ensuremath{\sim}2.3$ K. From the nuclear relaxation measurement, precise temperature-independent spin-lattice relaxation rates are observed at low temperatures under a weak magnetic field, indicating the gapless spin excitations. Further increasing the field intensity, we observe a spin excitation gap with the gap size proportional to the field intensity. These phenomena suggest a very unusual strongly correlated quantum disordered phase, and the implications for the quantum spin liquid state are further discussed.