Resonance fluorescence from atomic systems consists of a single spectral peak that evolves into a Mollow triplet for a strong excitation field. Photons from different peaks of the triplet show distinct photon correlation that make the fluorescence a useful light source for quantum information purpose. We characterize the fluorescence of a single optically trapped 87 Rb atom that is excited resonantly at different power levels. Second-order correlation measurements reveal the single photon nature of the fluorescence concurrently with Rabi oscillations of a strongly excited atom. The asymmetry in correlations between photons from two sidebands of the fluorescence spectrum when the atom is exposed to an off-resonant field further indicates that there is a preferred time-ordering of the emitted photons from different sidebands.