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Neutral hydrogen (HI) $21$-cm intensity mapping (IM) is a promising probe ofthe large-scale structures in the Universe. However, a few orders of magnitudebrighter foregrounds obscure the IM signal. Here we use the Tapered GriddedEstimator (TGE) to estimate the multi-frequency angular power spectrum (MAPS)$C_{\ell}(\Delta\nu)$ from a $24.4\,\rm{MHz}$ bandwidth uGMRT Band $3$ data at$432.8\,\rm{MHz}$. In $C_{\ell}(\Delta\nu)$ foregrounds remain correlatedacross the entire $\Delta\nu$ range, whereas the $21$-cm signal is localizedwithin $\Delta\nu\le[\Delta \nu]$ (typically $0.5-1\,\rm{MHz}$). Assuming therange $\Delta\nu>[\Delta \nu]$ to have minimal $21$-cm signal, we use$C_{\ell}(\Delta\nu)$ in this range to model the foregrounds. This foregroundmodel is extrapolated to $\Delta\nu\leq[\Delta \nu]$, and subtracted from themeasured $C_{\ell}(\Delta\nu)$. The residual $[C_{\ell}(\Delta\nu)]_{\rm res}$in the range $\Delta\nu\le[\Delta\nu]$ is used to constrain the $21$-cm signal,compensating for the signal loss from foreground subtraction.$[C_{\ell}(\Delta\nu)]_{\rm{res}}$ is found to be noise-dominated without anytrace of foregrounds. Using $[C_{\ell}(\Delta\nu)]_{\rm res}$ we constrain the$21$-cm brightness temperature fluctuations $\Delta^2(k)$, and obtain the$2\sigma$ upper limit $\Delta_{\rm UL}^2(k)\leq(18.07)^2\,\rm{mK^2}$ at$k=0.247\,\rm{Mpc}^{-1}$. We further obtain the $2\sigma$ upper limit $[\Omega_{{\rm HI}}b_{{\rm HI}}]_{\rm UL}\leq0.022$ where $\Omega_{{\rm HI}}$and $b_{{\rm HI}}$ are the comoving HI density and bias parametersrespectively. Although the upper limit is nearly $10$ times larger than theexpected $21$-cm signal, it is $3$ times tighter over previous works usingforeground avoidance on the same data.

Towards $21$-cm intensity mapping at $z=2.28$ with uGMRT using the tapered gridded estimator III: Foreground removal