i'm quite confused on how roman citizenship would be acquired by half "barbarian" romans (i.e gallo-romans or hispano-romans etc) since both parents needed to have citizenship for the son to be a true roman.
You might be interested in some earlier answers on these topics. There were many ways to become a Roman citizen, as u/Astrogator has written about in this thread on citizenship verification. Our u/J-Force has also described law tablets, with examples being about citizenship rights for communities in Gaul, here. Also relevant is perhaps an answer by our Astrogator about the Social War which mentions the Ius conubium, the right to marry Roman citizens that was granted to people with Latin rights