  We present an extended corona model based on ray-tracing simulations to
investigate X-ray time lags in Active Galactic Nuclei (AGN). This model
consists of two axial point sources illuminating an accretion disc that produce
the reverberation lags. These lags are due to the time delays between the
directly observed and reflection photons and are associated with the
light-travel time between the source and the disc, so they allow us to probe
the disc-corona geometry. We assume the variations of two X-ray sources are
triggered by the same primary variations, but allow the two sources to respond
in different ways (i.e. having different source responses). The variations of
each source induce a delayed accretion disc response and the total lags consist
of a combination of both source and disc responses. We show that the extended
corona model can reproduce both the low-frequency hard and high-frequency soft
(reverberation) lags. Fitting the model to the timing data of PG~1244+026
reveals the hard and soft X-ray sources at $\sim6r_{\text{g}}$ and
$\sim11r_{\text{g}}$, respectively. The upper source produces small amounts of
reflection and can be interpreted as a relativistic jet, or outflowing blob,
whose emission is beamed away from the disc. This explains the observed
lag-energy in which there is no soft lag at energies $<1$~keV as they are
diluted by the soft continuum of the upper source. Finally, our models suggest
that the fluctuations propagating between the two sources of PG~1244+026 are
possible but only at near the speed of light.
