"Mam" or ("Mieć" in dictionary ) requires Accusative. ( For Polish native speakers Accusative is the case that answers " Who / What do I have" )
I mixed it with Nominative because it "looks the same " for Nominative- Piwo, Accusative Piwo Genitive Piwa,
It's Accusative no matter what you have or who has it, I have piwo, you have piwo I have wódkę You have wódkę, They have wódkę (wódkę= Accusative of wódka)
full declension of Few Beers--Beers--Beer
N-Kilka Piw-----------Piwa----Piwo-Trochę Piwa
G-Kilku Piw-----------Piw------Piwa
D-Kilku Piwom-------Piwom--Piwu
A-Kilka Piw-----------Piwa-----Piwo
I--Kilkoma Piwami--Piwami--Piwem
L-Kilku Piwach------Piwom---Piwie
V-Kilka Piw-----------Piwa-----Piwo
Now what you ask is
I Have Adam's Beer
Mam piwo Adama. (Piwo in Accusative, Adam in Genitive),
Accusative often looks same as Nominative, (There are rules for it , and you will get there)
Don't overthink it. Rosetta throws you complicated things.