Does this type of stabilizer exist?
I don't know if such a structure actually exists, but I find it difficult to see why anybody would build one.

Firstly, placing the horizontal stabilisers at the top of two separate tail fins will require that each fin is strengthened to support the extra weight and the aerodynamic loads,

Secondly, there will probably be any number of aerodynamic issues around the joints between the components, each of which will be doubled.

Thirdly, in a real aeroplane you will have introduced substantial complexity into the control systems that have to manage all of this.

There may be other issues, but I see very little benefit aerodynamically or structurally to such a layout.

A conventional V-tail involves some control complexity, but does away with the weight of the vertical stabiliser. A T-tail retains the vertical stabiliser, but avoids control complexity, aerodynamic issues that may occur close to the engines, and can use the extra length to improve the leverage available to the horizontal stabiliser.

All that said, aircraft design is about compromise and utility. There may exist some powerful reason for adopting a sub-optimal layout to fulfil some specific purpose. You can see such an example in the design of the AN-225 Mriya which was originally built to transport the Soviet Buran spacecraft. The vertical stabilisers were moved to the ends of the horizontal stabilisers to keep the clear of the wake from the spacecraft riding piggy back. The 747 used to transport the US Space Shuttle had a similar modification, but retained the original vertical stabiliser.

Soviet Buran spacecraft during transport:



US Space Shuttle Atlantis during transport (image source: Wikipedia/NASA):