I'm afraid that whether you think of
Tonya as derived from
Antonia or as an alternate spelling of
Tanya, derived from
Tatiana, both of these go back to ancient
Roman names for which the original etymological meaning is simply unknown. Anything that can be said about either of them is simply a guess. Some guesses may be more educated than others, but until and unless someone finds more evidence from ancient writings, or deciphers the Etruscan language, the answer in terms of etymology must be "unknown".
This is a case where the use of the term "meaning" in regard to etymology may be misleading. The names
Anthony and
Tatiana didn't survive because of any original etymological connection, but because they were the names of
Christian saints. If I were you, I'd look up the lives of those saints and take their stories as the "meaning" for your name, because they are why the names are still in use today.
Of the etymologies suggested, the one that seems to at least come from an educated guess is "priceless". The "fairy queen" meaning comes from confusing
Tatiana with
Titania, the name of the fairy queen in Shakespeare's play
A Midsummer Night's Dream, so it is the one which is almost surely NOT correct as an etymology. The "
Flower" meaning, as the derivation for
Anthony given on this site says, is an ancient mistake made by confusing
Antonius with the Greek word for "flower". Since the spelling
Tonya does not include the "h", it really wouldn't be correct to use the "flower" meaning, though I suppose for
Anthony one could at least say the modern form has been blended with the Greek word for "flower".