We analyze the nucleosynthesis yields of various Type Ia supernova explosion simulations including pure detonations in sub-Chandrasekhar mass white dwarfs; double detonations and pure helium detonations of sub-Chandrasekhar mass white dwarfs with an accreted helium envelope; a violent merger model of two white dwarfs; and deflagrations and delayed detonations in Chandrasekhar mass white dwarfs. We focus on the iron peak elements Mn, Zn, and Cu. To this end, we also briefly review the different burning regimes and production sites of these elements, as well as the results of abundance measurements and several galactic chemical evolution studies. We find that super-solar values of Mn/Fe are not restricted to Chandrasekhar mass explosion models. Scenarios including a helium detonation can significantly contribute to the production of Mn, in particular the models proposed for calcium-rich transients. Although Type Ia supernovae are often not accounted for as production sites of Zn and Cu, our models involving helium shell detonations can produce these elements in super-solar ratios relative to Fe. Our results suggest a re-consideration of Type Ia supernova yields in galactic chemical evolution models. A detailed comparison with observations can provide new insight into the progenitor and explosion channels of these events.