I'll let someone who knows these coins give you a better answer, but for what it's worth, those are extremely common coins as ancients go. It wouldn't really be cost beneficial to fake those today as they can easily be had for under $20 for an average worn example. You might as well counterfeit something worth $50-200 or more for similar effort. Contemporary counterfeiting (meaning counterfeits made at the time of the legitimate coin) on the other hand has always existed, so sometimes you see those because at the time the relative worth of the coin was far more than now. Still, even today you see Chinese counterfeits of common date pre-WW2 coins that are worth less than $20, so you never know. So without knowing much about these coins specifically, I'd still be surprised to find out that it's fake, but it's possible however unlikely. The wear and damage looks appropriate for the age.
Your coin is fine. These are often faked, but the fakes are usually very easy to spot. They're more in the order of tourist trinkets. A sampling is below.
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