  (Abridged) In this paper, we present the results of an exceptional repeating
X-ray nuclear transient, eRASSt J045650.3-203750 (hereafter J0456-20),
uncovered by SRG/eROSITA in a quiescent galaxy at redshift of z~0.077. The main
results are: 1) J0456-20 cycles through four distinctive phases: an X-ray
rising phase leading into an X-ray plateau phase which lasts for ~2 months.
This is terminated by a rapid X-ray flux drop phase during which the X-ray flux
can drastically drop by more than a factor of 100 within 1 week followed by an
X-ray faint state for about two months before it starts the X-ray rising phase
again; 2) the X-ray spectra are generally soft in the rising phase with a
photon index >3.0, and become harder as the X-ray flux increases. There is
evidence of a multi-colour disk with inner region temperature of
$T_\text{in}=70$ eV at the beginning of the X-ray rising phase. The high
quality XMM-Newton data suggest that a warm and hot corona could be responsible
for the X-ray emission, through inverse Comptonisation of soft disk seed
photons, during the plateau phase and at the bright end of the rising phase; 3)
J0456-20 shows only moderate UV variability and no significant optical
variability; 4) radio emission is only detected (as yet) in the X-ray plateau
phase, and shows a rapid decline on a time-scale of 2 weeks. We conclude that
J0456-20 is likely a repeating nuclear transient with a tentative recurrence
time of ~223 days. We discuss several possibilities to explain J0456-20's
observational properties, and currently favour a repeating partial tidal
disruption event (TDE) as the most likely scenario. The long-term X-ray
evolution is explained as a transition between a thermal disk-dominated soft
state and a steep power-law state, implying that the corona can be formed
within a few months and destroyed within a few weeks.
