What you’re seeing is called fractional currency. The federal government issued a number of fractional bills during the Civil War. Find out why, and take a look at the mini-bills.
In November of 1861, the USS San Jacinto intercepted the RMS Trent. On board the Trent were two Confederate officials and one mail packet, all of them bound for England. Officials on the San Jacinto assumed that all three of these things would cause trouble for the already-troubled United States, and seized them. Of course, what would cause real trouble for the United States was war with Britain, which is what this incident was provoking.
Eventually the Trent Affair got smoothed over, but not before it really looked like the United States might be a thing of the past, which made United States currency not as valuable as it was before. The banks stopped exchanging gold for cash, people started speculating in silver coinage, and things went haywire in the economy.
To put a lid on the chaos, the United States Treasury issued postal currency. These were, essentially, “small change,” and they could be exchanged for real money as long as the amount of postal currency being exchanged was five dollars or less. The ability to conduct everyday transactions with the confidence that these special stamps could be exchanged for bills stabilized the situation, but it was a stop-gap measure. To prevent forgery, the Treasury started making fractional currency, in denominations of 3, 5, 10, 15, 25, and 50 cents. Each was roughly the size of six modern-day postage stamps. This currency stayed in circulation for a decade and a half. It was only in 1876 that it started getting replaced with coins again.
[Source: Bureau of Engraving and Printing]