Depending on your definition of firearms, there could be several answers.

Hand cannons were used widely in China in the 13th century. Powered by gunpowder ignition, small projectiles such as rocks or metal balls would be launched over short to medium distances. These could be reloaded with new powder and projectiles, and were relatively effective compared to their ease of use. Their effectiveness at range was low though. The techniques behind hand cannons spread to europe, and were the predecessors for later designs.

Before that, the Chinese made use of fire lances. These tubular devices would use gunpowder to release a load of small projectiles/burning material over very short distances. Early versions were often made of bamboo and were attached to regular lances, to be used as one-of firing devices. Later versions used metal tubes and ditched the lance. Fire lances appeared somewhere in the 10th or 11th century, but the first recorded usage in warfare was at the Siege of De'an in 1132.

Before that, stretching the definition quite a bit, the byzantines used a handheld device called a cheirosiphōn. These devices would use a pump system to propel flammable liquids (greek fire) over short distances. They could be ignited either afterwards, or possibly through a flame near the mouth of the device. These early handheld flamethrowers, and their non-handheld equivalents were used frequently in naval warfare and made the byzantine fleet very dangerous in close quarters under good weather conditions. These weapons are also described to be used against siege weapons and from siege weapons onto those defending city walls. These handheld devices were described as being used as early as the 10th century. Their non-handheld equivalents were in use for longer, as were 'grenades' made of pots filled with flammable liquids. Variations on the latter have seen use as early as the ancient Assyrians.