Does it make Sense for a Patriarchal system to exclusively have Female rulers?

If your world has female rulers, it is by definition a matriarchy, not a patriarchy.

 

True, it would depend on how much power the queen and regent actually have. Is all the real power in the hands of the regent, or does the queen have veto power? The queen may not have secular power, but her spiritual power could count for a lot if the society is very religious. Also, could women theoretically become politicians if they wanted to, or are they excluded from government by law? Can women vote? All of these will play a factor in how patriarchal the system really is, but officially, on its surface, it is still a matriarchal system, since women and only women are the rulers.

This doesn't mean that the society can't still have a patriarchal culture. Judging by the description, the society was truly matriarchal in the past, but has undergone cultural change since then, which shifted social power to the men, with the remaining matriarchal aspects being holdovers from the past.

 

Yes, but it does not ACTUALLY have female rulers, they barely seem to make any desicions based on what's described.

 

I agree with skip.knox, the terminology is inconsistent to what a prospective audience associates with the definition.

The system itself sounds fine. Sounds like a religious caste on one side and the administration on the other. The traditional Hindu system has the priests as caretakers of the temple, but don't have any administration control, whereas the kings have status but need the priests to confirm them. It's an interlocked system.

 

Maybe you might want to consider a slightly different approach. Don't worry too much about what tag fits best for what you're trying to do. Focus more on the power dynamics that you want to explore, the culture, the characters, and the interplay between them. Ask questions about how they manage and distribute power, what safeguards the society has against its abuse, and how these safeguards have been set in place. Then let the reader figure out if they would consider it a patriarchy or not. I find this approach frees me quite a bit to let my imagination fly, and I personally use it a lot for other such tags that might mean different things to different people.
Like "medieval", for example. Many people understand many different things by that word. And hey, medieval in Turkey is very different from medieval in Germany, or India, even if we have the LOOONG discussion as to what historical period is "medieval" exactly. So instead of asking if my world is medieval or not I ask what kind of tools they have access to and why, what materials, can they forge iron? Steel? Do they mostly build in wood? Stone? Thatch? Can they make some sort of concrete mix? How did they figure it out? Is it some crazy material in this world with particular properties that might do things that would make certain technological advancements irrelevant? Do they wear pointy hats with red feathers for some cultural reason? You will need to do different amounts of thinking depending on what you want to do with your story, but even if you just need a little bit, you can just focus on how things actually work in your world on more concrete terms, and then let your readers come to their own conclusions on how they want to label what you did.
This being said, labels are necessary, particularly if you want to find a wider audience. But you can figure them out by examining what you made and then coming to a conclusion, rather than by assuming a label first and then working to fit into it. Or at least that's what works for me. Did I go terribly off topic? I did, didn't I?