In my universe, there is a species from the Homo genus named Homo haematophagus (which means hematophagous human) (they are still humans, just not Homo sapiens) (their scientific name is a reference to the fact that they traditionally have a blood drinking ritual after sacrificing animals, and in a war, they often drank the blood coming from their rivals' wounds). They are commonly called vampires.
A weird thing about vampires is that they traditionally live in a patrilinear but matriarchal, unitary, absolute but elective monarchy. They reproduce by having babies, just like anatomically modern humans.
In the real world, the vast majority of human societies are both patrilinear and patriarchal. This is the case for the United States of America, the United-Kingdom of Great Britain and Northern Ireland, the Fifth French Republic, and Italy.
Most (all?) matrilinear and matriarchal human societies are now restricted to some isolated tribes.
However, there are human societies that are patriarchal but matrilinear, Jews (any Jewish diaspora, such as Ashkenazim, Sephardim, and Mizrahi), and Romani people are two famous examples (in the case of Jews, this is because traditionally, only men could be kohanim, and rabbis, but Jewish blood status is determined by the mother).
I have never heard about a matriarchal, but patrilinear human society (I however think that pre-colonial Madagascar could be a semi-example: there have been six Monarchs of Madagascar, the two thirds were queens, the other two were kings).
So, I wonder how a human society could be matriarchal but patrilinear (men inherit property and titles, but do not actually control it)?