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In this study, we present a comprehensive analysis of an unidentified point-like ultra-high-energy (UHE) $\gamma$-ray source, designated as 1LHAASO J1740+0948u, situated in the vicinity of the middle-aged pulsar PSR J1740+1000. The detection significance reached 17.1$\sigma$ (9.4$\sigma$) above 25$\,$TeV (100$\,$TeV). The source energy spectrum extended up to 300$\,$TeV, which was well fitted by a log-parabola function with $N0 = (1.93\pm0.23) \times 10^{-16} \rm{TeV^{-1}\,cm^{-2}\,s^{-2}}$, $\alpha = 2.14\pm0.27$, and $\beta = 1.20\pm0.41$ at E0 = 30$\,$TeV. The associated pulsar, PSR J1740+1000, resides at a high galactic latitude and powers a bow-shock pulsar wind nebula (BSPWN) with an extended X-ray tail. The best-fit position of the gamma-ray source appeared to be shifted by $0.2^{\circ}$ with respect to the pulsar position. As the (i) currently identified pulsar halos do not demonstrate such offsets, and (ii) centroid of the gamma-ray emission is approximately located at the extension of the X-ray tail, we speculate that the UHE $\gamma$-ray emission may originate from re-accelerated electron/positron pairs that are advected away in the bow-shock tail.