We present a Wideband Tapered Gridded Estimator (TGE), which incorporates baseline migration and variation of the primary beam pattern for neutral hydrogen (\({\rm H\hspace{0.5mm}}{\scriptsize {\rm I}}\)) 21-cm intensity mapping (IM) with large frequency bandwidth radio-interferometric observations. Here we have analysed \(394-494 \, {\rm MHz}\) \((z = 1.9 - 2.6)\) uGMRT data to estimate the Multi-frequency Angular Power Spectrum (MAPS) \(C_\ell(\Delta\nu)\) from which we have removed the foregrounds using the polynomial fitting (PF) and Gaussian Process Regression (GPR) methods developed in our earlier work. Using the residual \(C_\ell(\Delta\nu)\) to estimate the mean squared 21-cm brightness temperature fluctuation \(\Delta^2(k)\), we find that this is consistent with \(0 \pm 2 \sigma\) in several \(k\) bins. The resulting \(2\sigma\) upper limit \(\Delta^2(k) < (4.68)^2 \, \rm{mK^2}\) at \(k=0.219\,\rm{Mpc^{-1}}\) is nearly \(15\) times tighter than earlier limits obtained from a smaller bandwidth (\(24.4 \, {\rm MHz}\)) of the same data. The \(2\sigma\) upper limit \([\Omega_{{\rm H\hspace{0.5mm}}{\scriptsize {\rm I}}} b_{{\rm H\hspace{0.5mm}}{\scriptsize {\rm I}}}] < 1.01 \times 10^{-2}\) is within an order of magnitude of the value expected from independent estimates of the \({\rm H\hspace{0.5mm}}{\scriptsize {\rm I}}\) mass density \(\Omega_{{\rm H\hspace{0.5mm}}{\scriptsize {\rm I}}}\) and the \({\rm H\hspace{0.5mm}}{\scriptsize {\rm I}}\) bias \(b_{{\rm H\hspace{0.5mm}}{\scriptsize {\rm I}}}\). The techniques used here can be applied to other telescopes and frequencies, including \(\sim 150 \, {\rm MHz}\) Epoch of Reionization observations.