  Typical mechanisms to extract energies from a rotating black hole are the
Blandford-Znajek process and the Penrose process. The Penrose process requires
a special condition that is difficult to occur in common astrophysical
situations. However, the magnetic Penrose process (MPP) does not require such a
special condition, and can produce ultra-high energy cosmic rays. When neutrons
decay near a rotating black hole, the MPP efficiency of the produced proton is
maximized. The supermassive black hole in Sagittarius A* (Sgr A*) is likely to
have a radiatively inefficient accretion flow that is hot enough to produce
neutrons by nuclear reactions, which can be subsequently accelerated to
high-energy by the MPP. We calculate the production rate of accelerated protons
from the Sgr A* to estimated the gamma-ray flux at Earth produced by these
accelerated protons and the flux of the accelerated protons themselves
transported from Sgr A* to Earth. We find that these very high-energy gamma
rays ($E_{\gamma}\gtrsim10\,\mathrm{TeV}$) amount to a significant fraction of
the flux of the gamma-ray from the HESS J1745-290 and the central molecular
zone around $100\,\mathrm{TeV}$. The accelerated proton flux, when the
dimensionless spin parameter $a_{*}=0.5$ and the magnetic field strength in the
vicinity of the black hole $B_{0}=100\,\mathrm{G}$, is about $1.6-4.1\%$ of the
cosmic ray proton flux from KASCADE experiment at about $1\,\mathrm{PeV}$. Due
to the finite decay time of neutrons which need to be transported from the
accretion flow to the acceleration zone, our acceleration model can operate
only around black holes with mass not much greater than $\sim10^8\,M_\odot$.
