  In this first paper of the series, we present initial results of newly
upgraded Giant Meterwave Radio Telescope (uGMRT) observation of European
Large-Area ISO Survey-North 1 (ELAIS-N1) at 325 MHz with 32 MHz bandwidth.
Precise measurement of fluctuations in Galactic and extragalactic foreground
emission as a function of frequency as well as angular scale is necessary for
detecting redshifted 21-cm signal of neutral hydrogen from Cosmic Dawn, Epoch
of Reionization (EoR) and post-reionization epoch. Here, for the first time we
have statistically quantified the Galactic and extragalactic foreground sources
in the ELAIS-N1 field in the form of angular power spectrum using the newly
developed Tapered Gridded Estimator (TGE). We have calibrated the data with and
without direction-dependent calibration techniques. We have demonstrated the
effectiveness of TGE against the direction dependent effects by using higher
tapering of field of view (FoV). We have found that diffuse Galactic
synchrotron emission (DGSE) dominates the sky, after point source subtraction,
across the angular multipole range $ 1115 \leqslant \mathcal{\ell} \leqslant
5083 $ and $ 1565 \leqslant \mathcal{\ell} \leqslant 4754 $ for
direction-dependent and -independent calibrated visibilities respectively. The
statistical fluctuations in DGSE has been quantified as a power law of the form
$\mathcal{C}_{\mathcal{\ell}}= A \mathcal{\ell}^{-\beta} $. The best fitted
values of (A, $\beta$) are ($ 62 \pm 6$ $mK^{2}$, $2.55 \pm 0.3 $) and ($ 48
\pm 4$ $mK^{2}$, $2.28 \pm 0.4 $ ) for the two different calibration
approaches. For both the cases, the power law index is consistent with the
previous measurements of DGSE in other parts of sky.
