  We study phase-dependent fluctuations of the resonance fluorescence of a
single $\Lambda$-type three-level atom in the regime near coherent population
trapping, i.e., alongside the two-photon detuning condition. To this end, we
employ the method of conditional homodyne detection (CHD) which considers
squeezing in the weak driving regime, and extends to non-Gaussian fluctuations
for saturating and strong fields. In this framework, and using estimated
parameter settings of the resonance fluorescence of a single trapped $^{138}
\mathrm{Ba}^{+}$ ion, the light scattered from the probe transitions is found
to manifest a non-classical character and conspicuous asymmetric third-order
fluctuations in the amplitude-intensity correlation of CHD.
