We have a 2002 Hyundai Accent that misfires when it's cold. If it's hot, it runs fine, but you can still feel a lag when you accelerate from the stop. We replaced fuel pressure regulator, filter and cleaned the injector.
A lot of times, those noisy injectors flat and wear out when they get old and they need new injectors. What you want to do is have a mechanic, like one from YourMechanic, run a dealer-level scanner on it and analyze everything like the milliseconds in which the injectors are firing, the flow rate and all kinds of stuff that can be checked by a pro. You might need new injectors. That’s something that often wears out on these things. As old as it is, you might also have a wet and dry compression test on it, because if the engine is wearing out, the wet and dry compression will show it’s just flat wearing out and you just live with it. You probably are not going to want to rebuild the engine on it. It’s not worth it and it costs more money than the car is worth. Have your engine misfiring issue inspected by a certified technician, they will be able to recommend a repair so that you can get the most out of your car.