  Jellyfish galaxies are prototypical examples of satellite galaxies undergoing
strong ram pressure stripping (RPS). We analyze the evolution of 512 unique,
first-infalling jellyfish galaxies from the TNG50 cosmological simulation.
These have been visually inspected to be undergoing RPS sometime in the past 5
billion years (since $z=0.5$), have satellite stellar masses
$\mstarsat\sim10^{8-10.5}\,M_\odot$, and live in hosts with
$\mvir\sim10^{12-14.3}\,M_\odot$ at $z=0$. We quantify the cold gas
($T\leq10^{4.5}$ K) removal using the tracer particles, confirming that for
these jellyfish, RPS is the dominant driver of cold gas loss after infall. Half
of these jellyfish are completely gas-less by $z=0$, and these galaxies have
earlier infall times and smaller satellite-to-host mass ratios than their
gaseous counterparts. RPS can act on jellyfish galaxies over long time scales
of $\approx1.5-8$ Gyr. Jellyfish in more massive hosts are impacted by RPS for
a shorter time span and, at a fixed host mass, jellyfish with less cold gas at
infall and lower stellar masses at $z=0$ have shorter RPS time spans. While RPS
may act for long periods of time, the peak RPS period -- where at least 50
pecent of the total RPS occurs -- begins within $\approx1$ Gyr of infall and
lasts $\lesssim2$ Gyr. During this period, the jellyfish are at host-centric
distances $\sim0.2-2\rvir$, illustrating that much of RPS occurs at large
distances from the host galaxy. Interestingly, jellyfish continue forming stars
until they have lost $\approx98$ percent of their cold gas. For groups and
clusters in TNG50 $(\mvirhost\sim10^{13-14.3}\,M_\odot)$, jellyfish galaxies
deposit more cold gas ($\sim10^{11-12}\,M_\odot$) into halos than exist in them
at $z=0$, demonstrating that jellyfish, and in general satellite galaxies, are
a significant source of cold gas accretion.
