  We study the dynamics of an overdamped Brownian particle subjected to
Poissonian stochastic resetting in a nonthermal bath, characterized by a
Poisson white noise and a Gaussian noise. Applying the renewal theory we find
an exact analytical expression for the spatial distribution at the steady
state. Unlike the single exponential distribution as observed in the case of a
purely thermal bath, the distribution is double exponential. Relaxation of the
transient spatial distributions to the stationary one, for the limiting cases
of Poissonian rate, is investigated carefully. In addition, we study the
first-arrival properties of the system in the presence of a delta-function sink
with strength $\kappa$, where $\kappa=0$ and $\kappa=\infty$ correspond to
fully nonreactive and fully reactive sinks, respectively. We explore the effect
of two competitive mechanisms: the diffusive spread in the presence of two
noises and the increase in probability density around the initial position due
to stochastic resetting. We show that there exists an optimal resetting rate,
which minimizes the mean first-arrival time (MFAT) to the sink for a given
value of the sink strength. We also explore the effect of the strength of the
Poissonian noise on MFAT, in addition to sink strength. Our formalism
generalizes the diffusion-limited reaction under resetting in a nonequilibrium
bath and provides an efficient search strategy for a reactant to find a target
site, relevant in a range of biophysical processes.
