For over 20 years, the STAR experiment at Brookhaven National Laboratory's Relativistic Heavy-Ion Collider (RHIC) has worked to map the phase diagram of quantum chromodynamic (QCD) matter. Signatures of a deconfined phase of quarks and gluons have been observed in high energy Au+Au collisions. QCD matter is expected to undergo a continuous phase transition to this deconfined state at low baryon densities and a first-order phase transition at large baryon densities, with a critical point marking the endpoint in the phase diagram of the first-order phase transition curve. The experimental search for signatures of a QCD critical point is underway at RHIC in STAR's Beam Energy Scan (BES) program. Fluctuations in the number of protons detected in heavy-ion collisions is one such observable, as a critical point is expected to enhance fluctuations of conserved charges such as baryon number.This dissertation presents measurements of proton-number fluctuations in STAR's fixed-target program at √sNN = 3.2$, 3.5, 3.9, and 4.5~GeV in order to search for signatures of a QCD critical point. These fluctuations are quantified by cumulant ratios and factorial cumulant ratios of event-by-event proton-number distributions. No evidence of a QCD critical point is observed in the fourth-order (factorial) cumulant ratios. However, large deviations from the non-critical baseline are reported in the second and third-order (factorial) cumulant ratios. Implications for the QCD critical-point search are discussed
