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Andes Large-area PArticle detector for Cosmic-ray physics and Astronomy (ALPACA) is an international experiment that applies southern very-high-energy (VHE) gamma-ray astronomy to determine the origin of cosmic rays around the knee energy region ($10^{15}\, {\rm eV} - 10^{16}\, {\rm eV}$). The experiment consists of an air shower (AS) array with a surface of $83, 000\, {\rm m}^2$ and an underground water Cherenkov muon detector (MD) array covering $5, 400\, {\rm m}^2$. The experimental site is at the Mt. Chacaltaya plateau in La Paz, Bolivia, with an altitude of $4, 740\, {\rm m}$ corresponding to $572\, {\rm g}/{\rm cm}^2$ atmospheric thickness. As the prototype experiment of ALPACA, the ALPAQUITA experiment aims to begin data acquisition in late 2021. The ALPAQUITA array consists of a smaller AS array ($18, 450\, {\rm m}^2$) and underground MD ($900\, {\rm m}^2$), which are now under construction. ALPAQUITA's sensitivity to gamma-ray sources is evaluated with Monte Carlo simulations. The simulation finds that five gamma-ray sources observed by H.E.S.S. and HAWC experiments will be detected by ALPAQUITA beyond 10 TeV and one out of these five - HESS J1702-420A - above 300 TeV in one calendar year observation. The latter finding means that scientific discussions can be made on the emission mechanism of gamma rays beyond 100 TeV from southern sources on the basis of the observational results of this prototype experiment., This is the manuscript accepted by Experimental Astronomy. For the published article, see https://doi.org/10.1007/s10686-021-09796-8