The history of printed money is as old, in some ways older, than minted
money. Before coins were invented in about 660BCE, when trade was
basically barter, and goods and products were traded back and forth
between tradesmen, artisans, citizens and officials, excess goods were
stored at home, or in community warehouses or other public facilities.
This necessitated the development of methods to keep track of who had what
stored where - leading to the development of writing itself.
The earliest clay-tablet storage records so far discovered were small, usually square, relatively thin, bits of clay with a few symbols representing various products and their quantity pressed into the clay and given as receipts to the people depositing their produce in common warehouses. Since these products were fungible; i.e. exactly alike, its probable that from the first day, people owning such receipts began to trade them for goods or other receipts for different stored products owned by other people. These exchanges would have been much more convenient than trying to carry large quantities of products home, to a shop, or from one storage location to another. Thus, with little conscious recognition, and no doubt crude by modern standards, hand-printed (albeit on clay) money was born. Only later, when tradesmen realized some highly-regarded metals, especially gold and silver, could be traded for just about any product would coins have been invented.
Although "paper money" is a term used to describe most government and institutional printed money, the term is a misnomer. It would be far more accurate to refer to banknotes as "printed money", because can also be found made of clay, wood, pounded bark, cloth, leather, parchment, metal foils, and in recent years, plastic with paper-like characteristics. Printed or written money as we know it is nothing more than a receipt for goods, services or labour, which can be traded for other goods, services or labour in lieu of coins or specie.