Okay kiddo, so the Hasmonean coinage is money that was made a long time ago by a group of people called the Hasmoneans. They were in charge of a place called Judea, which is where Israel is now.
Now, imagine you have a toy that you really like and you want to trade it for something else. You need something to use to trade, right? That's what money is. And the Hasmoneans needed money so they made their own!
They made these coins out of metal, like gold and silver. They put a picture of a person or animal on one side, and writing in Hebrew on the other side. The writing told people who made the coin and how much it was worth.
People liked the Hasmonean coins because they were pretty and valuable. They could use them to buy things they needed, like food or clothes.
But eventually, the Hasmoneans weren't in charge anymore and people stopped using their coins. Today, some people collect Hasmonean coins because they are really old and interesting to look at.
So that's the story of the Hasmonean coinage - money made a long time ago by the people who ruled Judea, with pictures and writing on them to show their value!