The production of the p-process nuclides that we observe today in the Solar Systemis still uncertain. Recent Galactic Chemical Evolution (GCE) calculations, showedthat explaining the inventory of the p-nuclides by the contribution from Core col-lapse supernovae (ccSNe) alone is challenging, thus requiring a complementary con-tribution from thermonuclear supernovae (SNe Ia), assuming in this last case ans-process rich pre-explosive seeds distribution, built byneutron captures during theaccretion phase. Presently there are no complete stellar models calculating theseabundances. We calculate accreting white dwarfs (WDs) models with five differentinitial masses using the stellar code MESA. We then focus on the nucleosynthesiscalculating the full abundance distribution. In these models the dominant neutronsource are22Ne(α,n)25Mg, activated at the bottom of the convective thermal pulsedriven by the Helium flashes along the accretion phase, for WDmasses lower than1.26 M⊙, and13C(α,n)16O for WD masses equal or higher than 1.26 M⊙. We foundneutron densities up to few 1015cm−3in the most massive WDs. In particular, weobtain a strong production by neutron captures up to the Pb region, showing howthe classic assumption of a neutron-capture rich pre-explosive seeds distribution isjustified. Using these results, we compute the resulting explosive nucleosynthesis ofproton rich heavy stable isotopes using a multi-D SNe Ia model, and discuss the un-certainties affecting our results, focusing in particular on the nuclear reaction-rateswhich provide the dominant contribution to the production uncertainty, highlightingwhich of the identified key reactions are realistic candidates for future experiments.