  The production of strange~($K^0_S$, $\Lambda$) and multi-strange~($\Xi$ and
$\Omega$) hadrons in jets and underlying events in \pp and \pPb collisions is
studied with ALICE at the LHC. Transverse momentum ($p_\rm{T}$) differential
density distribution of particles produced in a jet is compared to that of
inclusive particle production and that in underlying events. The particle yield
ratios of $\Lambda/K^0_S$ and $\Xi/\Lambda$ as a function of $p_\rm{T}$ are
also investigated in jets and underlying events.The production of the
multi-strange hadrons, $\Xi$ and $\Omega$, and the corresponding ratio in jets
and underlying events are measured for the first time. The
$p_\rm{T}$-differential density distribution of hadrons associated with hard
scattering decreases slower than that for inclusive production. The
baryon-to-meson and baryon-to-baryon ratios measured in jets exhibit clear
differences from values obtained from the inclusive spectra in the intermediate
$p_\rm{T}$ range. The $p_\rm{T}$ distribution of strange hadrons produced in
jets is also studied in pp collisions at $\sqrt{s}$ = 13 TeV and 7 TeV and in
p-Pb collisions at $\sqrt{s_\rm{NN}}$ = 5.02 TeV. The $p_\rm{T}$ spectra of
particle produced in jets are independent of collision systems and collision
energies.No apparent collision energy and collision system dependence is
observed for the particle yield ratios of $\Lambda/K^0_S$ and $\Xi/\Lambda$
associated with energetic jets. These new results are compared to PYTHIA 8
event generator. The $\Lambda/K^0_S$ ratio are generally reproduced by the
model, but large discrepancies between data and PYTHIA simulations are observed
for $\Xi/\Lambda$.
