I got a coin from my father as a gift but neither he or me are expert so I like to know whether it is fake and if not what would be the value? I weighted the coin in a jewlery shop and it was 13.7 but the surface patina looks not natural to me.
Not my time period but I know you should include size as well, it makes it easier for others to determine more about the coin.
It's a tetradrachm of Nero and Agrippina minor https://www.acsearch.info/search.html?id=4698504 https://www.acsearch.info/search.html?id=4543617
The style is absolutely right for that issue, as is the weight and size. It appears to be struck and not cast. The toning is a little weird, to be sure, but not out of the realm of what is seen. Here's an Alexandrian tetradrachm -- with admittedly much more base metal than this one from Antioch -- with a lot of reddish tones: