We study the resonance fluorescence of a system with angular momentum J = 1/2−J = 1/2 level structure driven by a single, linearly polarized, monochromatic laser field. Quantum interference among the two, antiparallel, π transitions leads to rich results. We develop the article around two broad overlapping themes: (i) the observation of quantum beats in the intensity and the dipoledipole, intensity-intensity, and quadrature-intensity correlations, when the atom is subject to a strong laser and large Zeeman splittings. The mean and modulation frequencies of the beats are given by the average and difference, respectively, among two close generalized Rabi frequencies related to a Mollow-like spectrum with two pairs of sidebands. (ii) The nonclassical and non-Gaussian properties of phase-dependent fluorescence for the cases of weak to moderate excitation and in the regime of beats. The fluorescence in the beats regime is nonclassical, mainly from the third-order dipole fluctuations, which reveal them to be also strongly non-Gaussian. For weak to moderate driving laser and small detunings and Zeeman splittings the nonclassicality is an interplay of second-(squeezing) and third-order dipole noise.