  Fluctuations of the baryon number in relativistic heavy-ion collisions are a
promising observable to explore the structure of the QCD phase diagram. The
cumulant ratios in heavy ion collisions at intermediate energies
($\sqrt{s_{\textrm{NN}}} < 7$ GeV) have not been studied to date. We
investigate the effects of mean field potential and clustering on the cumulant
ratios of baryon and proton number distributions in Au+Au collisions at beam
energy of 1.23 GeV$/$nucleon as measured by the HADES Collaboration at GSI.
Ultrarelativistic Quantum Molecular Dynamics (UrQMD) and the JAM model are used
to calculate the cumulants with different mean field potentials. It is found
that the cumulant ratios are strongly time dependent. At the early stage, the
effects of the potentials on the fluctuations of the particle multiplicity in
momentum space are relatively weak. The mean fields enhance the fluctuations
during the expansion stage, especially for small rapidity acceptance windows.
The enhancement of cumulant ratios for free protons is strongly suppressed as
compared to that for all baryons. The mean field potentials and the clustering
play an important role for the measured cumulant ratios at intermediate energy.
