This randomly came to me on the way home, but still concerns me

No??? Maybe? Find out in Persona 6

What shadow had a persona?

Spoiler alert

Teddie did.

Oh must have slipped my brain. But if a shadow can have a shadow a persona must be able to have a persona

I suppose if you put it that way it kinda makes sense

Plus, Personas seem to have their own consciousness. For example, in Persona 2, characters sometimes mention their Personas feeling a certain way. And we know for a fact they can talk (in the initial contract at the very least).

Teddie had a Shadow/Persona because he awakened to an ego, aka, he became more than just a Shadow, but a "person".
That ego takes the form of a Shadow/Persona so....

No a Persona can't have a Persona

So couldn't a Persona awaken to an ego themselves?

Personas and Shadows are fundamentally different entities. Just take the way they act in P4 as an example. Shadows in a sense are "separate" or want to be their own thing in cases, while a Persona is the "same" as the user, they work together.
If anything a Persona's "Persona" is its own user if you wanna think of it that way.

or something
idk Teddie is fucking stupid anyway

That makes sense. A Persona's Persona is its user... or something like that. Idk Personas are weird

A fair point, but don't use your bias against Teddie as an argument

I wasn't using my bias against Teddie as an argument I was basically using it as a joke to get across that
I don't understand how this works and Teddie's story doesn't actually make a lot of sense so I'm trying to fill in holes based on my own assumptions