"posit" just means "placed", so "posit," as such, would be absolutely 100% wrong and irrelevant here.
From your new edit:
This sentence "To posit something is to suppose it exists (it may or may not exist)." is completely 100% incorrect in English.
To "posit" just means "make a suggestion" or "let's assume for the sake of discussion...".
For example, I could "posit" that we take a holiday in Cremona. Or, I could posit that "X exists". Or I could posit that "X does not exist". Or I could posit Mr Smith as Mayor and then we could discuss, under that posit, what that would be like.
For me, it would be a shame to invent a word similar to "posit".
For the position "???" I believe you mean:
"possibly exists"
Is that correct?
If you had to invent a term, what about possexistspossexists?
{Obviously, philosophical questions arise such as "Is 'does exist' any different I also suggest potentialiates. ("Potential" made in to a verb.)
taking a cue from 'exists'?"potential field" and similar subjects in quantum physics." But as
(There is a danger though, that since it is a matter of philosophy you saymay distinguish between potentially existing and possibly existing!!)
Footnote - earlier the word "posits" was discussed. That simply means "make a suggestion" or "let's assume for the sake of discussion.. it's philosophy.}", so posit-like words would be confusing.