Galaxy Telpha Z was a region of space, home to the planet Metamorpha.

In 2266, the USS Enterprise explored this region, discovering the planet Metamorpha. (TOS comic: "The Peril of Planet Quick Change")

It is unlikely that this region could be an actual galaxy, as the Enterprise could not leave the Milky Way Galaxy and travel to another under standard warp drive in any reasonable amount of time. Therefore, it is likely that this is simply the name for a sector or region of the Milky Way, presumably within the Alpha or Beta Quadrants.
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