This expression means; To expect special treatment.

It is assumed that this expression goes far back into the Baroque
period, where it was quoted by Abraham a Santa Clara (1644-1709),
a famous Augustinian preacher. The origin of this saying might be
explained by the fact that poor people could not afford sausages in
the Middle Ages. Sausages and butter were once particularly
expensive and valuable, and were therefore considered a delicacy.
Occasionally, poorer families were offered a sausage as a gift, which
was considered by some to be special treatment. Being given an
extra sausage was equivalent to receiving a special favour. This
idiom carries negative connotations. If someone said to you “Jetzt
verlangst du aber eine Extrawurst!” (“Now you’re asking for extra
sausage!”) they would be suggesting that you are requesting
something that you do not deserve.