  We report a measurement of cumulants and correlation functions of
event-by-event proton multiplicity distributions from fixed-target Au+Au
collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV measured by the STAR experiment.
Protons are identified within the rapidity ($y$) and transverse momentum
($p_{\rm T}$) region $-0.9 < y<0$ and $0.4 < p_{\rm T} <2.0 $ GeV/$c$ in the
center-of-mass frame. A systematic analysis of the proton cumulants and
correlation functions up to sixth-order as well as the corresponding ratios as
a function of the collision centrality, $p_{\rm T}$, and $y$ are presented. The
effect of pileup and initial volume fluctuations on these observables and the
respective corrections are discussed in detail. The results are compared to
calculations from the hadronic transport UrQMD model as well as a hydrodynamic
model. In the most central 5\% collisions, the value of proton cumulant ratio
$C_4/C_2$ is negative, drastically different from the values observed in Au+Au
collisions at higher energies. Compared to model calculations including Lattice
QCD, a hadronic transport model, and a hydrodynamic model, the strong
suppression in the ratio of $C_4/C_2$ at 3 GeV Au+Au collisions indicates an
energy regime dominated by hadronic interactions.
