How to get the electronic resident permit card instead of a stamp into my passport?

Please note that in general neither SERS or you have the choice to select how the residence permit should be issued by the Immigration Office. The German authorities decide along with their capacities whether the residence permit is issued as a stamp/label into the passport or as card. 

The residence permit card is NOT an ID card, which means that also the card needs to be carried always together with the passport.

Both residence permit types are the same under Immigration Law and contain the same rights and duties.