  The prevalence of short-period super-Earths that are independent of host
metallicity challenges the theoretical construction of their origin. We propose
that dust trapping in the global pressure bump induced by magnetospheric
truncation in evolved protoplanetary discs (PPDs) around T Tauri stars offers a
promising formation mechanism for super-Earths, where the host metallicity is
already established. To better understand this planet forming scenario, we
construct a toy inner disc model and focus on the evolution of dust trapped in
the bump, taking into account the supply from drifting pebbles and loss due to
funnel flows. We develop an implicit coagulation-fragmentation code,
$\mathtt{Rubble}$, and perform a suite of simulations to evolve the local dust
size distributions. Our study for the first time considers dust feedback effect
on turbulent diffusion in this kind of model. We report that efficient dust
growth and significant accumulation of dust mass is possible in less turbulent
disc with sturdier solids and with faster external supply, laying out a solid
foundation for further growth towards planetesimals and planetary embryos. We
further find that, depending on the dominant process, solid mass may
predominantly accumulate in cm-sized grains or particles in runaway growth,
indicating different ways of forming planetesimals. Furthermore, these various
outcomes show different efficiencies in saving dust from funnel flows,
suggesting that they may be distinguishable by constraining the opacity of
funnel flows. Also, these diverse dust behaviours may help explain the observed
dipper stars and rapidly varying shadows in PPDs.
