### Abstract:

Neutral hydrogen (H I) 21-cm intensity mapping (IM) offers an efficient technique for mapping the large-scale structures in the Universe. We introduce the 'Cross' Tapered Gridded Estimator (Cross TGE), which cross-correlates two cross-polarizations (RR and LL) to estimate the multifrequency angular power spectrum Cι(Δν). We expect this to mitigate several effects like noise bias, calibration errors, etc., which affect the 'Total' TGE that combines the two polarizations. Here, we apply the Cross TGE on 24.4-MHz-bandwidth uGMRT (upgraded Giant Metrewave Radio Telescope) Band 3 data centred at 432.8 MHz aiming H I IM at z = 2.28. The measured Cι(Δν) is modelled to yield maximum likelihood estimates of the foregrounds and the spherical power spectrum P(k) in several k bins. Considering the mean squared brightness temperature fluctuations, we report a 2σ upper limit Δ2UL(k) ≤ (58.67)2 mK2 at k = 0.804 Mpc−1, which is a factor of 5.2 improvement on our previous estimate based on the Total TGE. Assuming that the H I traces the underlying matter distribution, we have modelled Cι(Δν) to simultaneously estimate the foregrounds and [ΩH IbH I], where ΩH I and bH I are the H I density and linear bias parameters, respectively. We obtain a best-fitting value of [ΩH IbH I]2 = 7.51 × 10−4 ± 1.47 × 10−3 that is consistent with noise. Although the 2σ upper limit [ΩH IbH I]UL ≤ 0.061 is ∼50 times larger than the expected value, this is a considerable improvement over earlier works at this redshift.