We studied the effects of centrality fluctuation and deuteron formation on the cumulant (Cn) and correla-tion functions (κn) of protons up to the sixth order in the most central (b＜ 3 fm) Au+Au collisions at √SNN =3 GeV in a microscopic transport model (JAM).The results are presented as a function of rapidity acceptance within the transverse momentum 0.4 ＜ PT ＜ 2 GeV/c.We compared the results obtained by the centrality bin width correction(CBWC) using charged reference particle multiplicities with the CBWC using impact parameter bins.It was found that,at low energies,the centrality resolution for determining the collision centrality using charged particle multipli-cities is not sufficient to reduce the initial volume fluctuation effect for higher-order cumulant analysis.New meth-ods need to be developed to classify events with high centrality resolution for heavy-ion collisions at low energies.Finally,we observed that the formation of deuterons suppresses the higher-order cumulants and correlation func-tions of protons and found it to be similar to the efficiency effect.This work can serve as a noncritical baseline for the QCD critical point search in the high baryon density region.