We have searched for evidence of physics beyond the standard model in events that include an energetic photon and an energetic b-quark jet, produced in 85 pb(-1) of (p) over barp collisions at 1.8 TeV at the Tevatron Collider at Fermilab. This signature, containing at least one gauge boson and a third-generation quark, could arise in the production and decay of a pair of new particles, such as those predicted by supersymmetry, leading to a production rate exceeding standard model predictions. We also search these events for anomalous production of missing transverse energy, additional jets and leptons (e, mu and tau), and additional b quarks. We find no evidence for any anomalous production of gammab or gammab + X events, We present limits on two supersymmetric models: a model where the photon is produced in the decay (χ) over tilde (0)(2)-->gamma(χ) over tilde (0)(1), and a model where the photon is produced in the neutralino decay into the gravitino LSP, (χ) over tilde (0)(1)-->gamma(G) over tilde. We also present our limits in a model-independent form and test methods of applying model-independent limits.