  Extreme blazars have exceptionally hard intrinsic X-ray/TeV spectra and
extreme peak energies in their spectral energy distribution (SED).
Observational evidence suggests that the non-thermal emission from extreme
blazars is typically non-variable. We aim to explore X-ray and GeV
observational features of a variety of extreme blazars and also aim to test the
applicability of various blazar emission models that could explain the very
hard TeV spectra. We perform X-ray analysis of AstroSat and Swift-XRT data,
along with gamma-ray data from Fermi-LAT, for sources; 1ES 0120+340, RGB
J0710+591, 1ES 1101-232, 1ES 1741+196 and 1ES 2322-409. We employ three models:
1) a steady-state one-zone synchrotron-self-Compton (SSC) code, 2) another
leptonic scenario of co-accelerated electrons and protons on multiple shocks,
applied only on the extreme-TeVsources and 3) a one-zone hadro-leptonic
(OneHaLe) code. The hadro-leptonic code is used twice to explain the gamma-ray
emission process: proton synchrotron and synchrotron emission of secondary
pairs. Our X-ray analysis provides well-constrained estimates of the
synchrotron peak energies for both 1ES0120+340 and 1ES1741+196. The multi-epoch
X-ray and GeV data reveal spectral and flux variabilities in RGB J0710+591 and
1ES 1741+196, even on time scales of days to weeks. As anticipated, the
one-zone SSC model adequately reproduces the SEDs of regular HBLs but
encounters difficulties in explaining the hardest TeV emission. Hadronic models
offer a reasonable fit to the hard TeV spectrum, though with the trade-off of
requiring extreme jet powers. On the other hand, the lepto-hadronic scenario
faces additional challenges in fitting the GeV spectra of extreme-TeV sources.
Finally, e-p co-acceleration scenario naturally accounts for the observed hard
electron distributions and effectively matches the hardest TeV spectrum of RGB
J0710+591 and 1ES 1101-232.
