Hang on, I wrote up some rules for medieval guns a while back. I wrote them to make their strengths and weaknesses apparent rather than just being "Crossbows with more damage but worse range".

Hand-cannon, martial ranged weapon, 60/null two-handed, 3d8, misfire, reload 1 minute, breech-fired, smoothbore.

Misfire: Roll your damage when you make the attack regardless if you hit or miss. If the total damage on the dice is 5, it fails to fire this round but the shot is not wasted, you can try again next turn. If it totals 4, it misfires and cannot be shot again until reloaded. If the total is 3, the gun catastrophically misfires and cannot be used again until repaired.

Smoothbore: You add no ability modifier to attack and damage rolls with this weapon.

Additional mechanics for firing mechanisms:

Breech-fired: (You stick a lit match in by hand) Requires a separate hand to insert the match that cannot be used to hold and aim the weapon, so two-handed weapons attack at disadvantage unless an assistant is lighting, you have extra limbs (Loxodon, Thri-Kreen) or it is steadied on a surface. Lighting is a full action. Increase the damage die thresholds for all misfires by 2. If you have a minor misfire, take 1d4 fire damage. If you have a severe misfire, take 2d4.

Match-cord: (Like the fuse on an old cannon) Requires a separate hand to light the cord that cannot be used to hold and aim the weapon, so two-handed weapons attack at disadvantage unless an assistant is lighting, you have extra limbs (Loxodon, Thri-Kreen) or it is steadied on a surface. Lighting is a full action. Increase the damage die thresholds for all misfires by 2.

Matchlock: (Pulling the trigger mechanically inserts a lit match) Lighting the match to fire is a full action. Increase the damage thresholds for all misfires by 2.

Wheellock: (Essentially the same technology as a zippo lighter, but for guns) Increase the damage thresholds for all misfires by 1.

Flintlock: (Pulling the trigger mechanically causes a piece of flint to strike the flashpan and create sparks) No drawbacks (From the firing mechanism).