GRB 160802A is one of the brightest gamma-ray bursts (GRBs) observed by the Fermi Gamma-ray Burst Monitor (GBM) in the energy range of 10-1000 keV, while at the same time it is surprisingly faint at energies greater than or similar to 2 MeV. An observation with the AstroSat/CZT Imager also provides the polarization that helps in constraining different prompt emission models using the novel joint spectra-polarimetric data. We analyze the Fermi/GBM data, and find two main bursting episodes that are clearly separated in time, one of which is particularly faint in higher energies and having certain differences in their spectra. The spectrum in general shows a hard-to-soft evolution in both the episodes. Only the later part of the first episode shows intensity tracking behavior corresponding to multiple pulses. The photon index of the spectrum is hard, and in over 90% cases, crosses even the slow cooling limit (alpha = -2/3) of an optically thin synchrotron shock model. Though such hard values are generally associated with a sub-dominant thermal emission, such a component is not statistically required in our analysis. In addition, the measured polarization in 100-300 keV is too high, pi = 85 +/- 29%, to be accommodated in such a scenario. Jitter radiation, which allows a much harder index up to alpha = + 0.5, in principle can produce high polarization, but only beyond the spectral peak, which in our case lies close to 200-300 keV during the time when most of the polarization signal is obtained. The spectro-polarimetric data seems to be consistent with a subphotospheric dissipation process occurring within a narrow jet with a sharp drop in emissivity beyond the jet edge, and viewed along its boundary