The half Reale in question appears to be real - grades VG to Fine and is about average for an 1855 from Zacatecas. They are worth somewhere in the $5 to $10 range.
The coin would have been legal tender in the US until 1857 and was worth 6 1/4 cents US. The 8 Reale system developed in Spain was the basis of the US dollar but in the states they used decimals of the dollar and not 1/8ths. The stock market still uses the 1/8ths system a holdover from 2 centuries ago.
The 1/2 reale is a 1/16th of a dollar. If you have ever hear the expression "Two bits" it is a reference to a 2 Reale coin. There are 8 bits to the dollar (each bit is 1 reale). This goes back to colonial times when you could make change by cutting an 8 Reale coin into "bits" - half a coin 4 bits - a quarter was 2bits, etc.
According to J.L. Riddell who was the melter and refiner for the US mint in New Orleans before the Civil War - Spanish American coins (primarily Mexican) constituted 90% of the silver coins in circulation in Louisiana in 1845. So this little Mexican coin has a great claim to actually being an early US Republican coin.