  Measurement of fluctuations in diffuse HI 21 cm background radiation from the
post-reionization epoch (z < 6) is a promising avenue to probe the large-scale
structure of the Universe and understand the evolution of galaxies. We observe
the European Large-Area ISO Survey-North 1 (ELAIS-N1) field at 300-500 MHz
using the upgraded Giant Meterwave Radio Telescope (uGMRT) and employ the
'foreground avoidance' technique to estimate the HI 21 cm power spectrum in the
redshift range z = 1.96-3.58. Given the possible systematics that may remain in
the data, we find the most stringent upper limits on the spherically averaged
21 cm power spectra at k~1.0 Mpc$^{-1}$ are (58.87 mK)$^2$, (61.49 mK)$^2$,
(60.89 mK)$^2$, (105.85 mK)$^2$ at z = 1.96,2.19,2.62 and 3.58, respectively.
We use this to constrain the product of neutral HI mass density (Omega_HI) and
HI bias (b_HI) to the underlying dark matter density field, [Omega_HI*b_HI], as
0.09,0.11,0.12,0.24 at z=1.96,2.19,2.62,3.58, respectively. To the best of our
knowledge these are the first limits on the HI 21 cm power spectra at the
redshift range z = 1.96 - 3.58 and would play a significant role to constrain
the models of galaxy formation and evolution.
