I don't know your year model, my 2001 has a fuel pump module in gas tank. Access is under back seat. I had to replace mine last year. It costs a little more than a filter, but only a few bolts and complete unit can be replaced. This is the one I replaced for mine. Module has everything needed for fuel pump.
My 2013 Hyundai Elantra has developed a problem. There is a noticeable miss (or bump) when the car is in idle reverse or idle forward. It is worse in reverse. When you slightly rev the engine the problem goes away. The car has about 40,000 miles on it.
Does this sound like a fuel system issue (e.g., fuel pump or fuel filter) or a transmission issue?
I will warn you that once I get some direction I will probably ask some more questions.