I have a problem when putting gas in the car

Hello. Yes, there is a reason why this is happening. There is a valve near the gas tank that is part of the Evap System. The Evap system takes the vapors out of the gas tank and draws them into the engine to burn them, this is to lower emissions. The valve I'm referring to is called a Vent Valve, it is supposed to open when the vehicle is shut off. When it doesn't open, (they get stuck closed when they fail or due to an electrical problem) there is no place for the fuel vapor to go when you are filling up with gas. And this causes the handle at the gas station to click off. The handle at the gas station is doing exactly what it's supposed to do, but since the fuel vapors can't escape through the vent valve, the handle will continue to click off. I will get some wiring diagrams and the location of the valve on your particular vehicle.

Okay, Hyundai's information may not be exactly correct on some of the aftermarket databases which we use. They are saying the Vent Valve closes when the engine is shut off. Which I do not think is correct. But either way, the refueling issue is caused by the same problem. The Fuel Vapors are not allowed to go where they need to go. On a conventional Evap system the vent valve opens when the vehicle is shut off for refueling purposes. You will notice on the diagrams below #1 and #4 are the same system but look different. I believe the #4 is correct, the Valve marked "CCV" is the canister vent valve, if it is stuck closed. You will have a lot of trouble refueling. The reason why there is no check engine light yet, is because the system has not run its self-tests and/or has run its self-tests where it would close that valve anyway to pressure or vacuum the system to check for leaks.
It has not set a circuit code for the valve yet because it may be activating the valve to close it and it's already closed so the system doesn't see a problem. It will eventually set a code because it will fail a self-test at some point. It takes certain conditions to run its self-tests.

I have seen this problem many times and know that there is a blockage or valve not opening allowing refueling. The Canister Vent Valve is not expensive, they go bad all the time, so if you take this to a shop, you know what's happening. And they can't talk you into a new engine. Just a joke. But this way they can't sell you unnecessary parts. Granted it might be a Fuel filler neck problem, since the information is not perfectly clear on which design it is, but it's still a vapor issue not allowing refueling. I hope this helps some.

https://www.2carpros.com/articles/how-emission-control-systems-work

Okay. So, I did a little more checking and there are actually some Technical Service Bulletins on some of the Evap System components. Now even though your vehicle is not setting any codes yet. The components on these TSBs definitely can cause the fault you're having. Sometimes with these Bulletins they do not always send any documentation out to each customer. Which they should in my opinion.

The first one (pages 1 and 2) is for the Evap Canister cracking where it bolts up to the vehicle, this is not the issue with your vehicle, but they should still honor the TSB and do this repair for you. The 2nd one (pages 3 and 4) has to do with the gas filler neck air filter. Now this can cause the issue you are having. It might not be reaching the code setting criteria since the system is not detecting a Restricted vent circuit. There could be an issue with the gas filler neck itself blocking the flow of air coming back out. If the filler tube cannot allow air to exit the filler tube it can cause a filling issue. Since they posted Technical Service Bulletins, that means that they are seeing enough problems in this area to post a repair from the dealership for it.
So, you may be able to have the dealership fix this for free. Which would be good.

The problem could be in the Fuel shut off valve, the 2 way and cut valve, or something in the filler neck. In the last diagram, in green is where the fuel vapors are supposed to be forced into. If any of these valves are sticking or stuck closed it will cause these issues.
Sometimes when people over fill their gas tanks, problems like this can show up. I'm sure you have seen people pull the gas handle out a little bit more at the gas station to try to fill their tanks as much as possible. Well, this is over filling the tank, the system is designed to click off when the tank is filled to its max level. But when over filling occurs, Evap canisters can get liquid gas in them, cut valve can get stuck closed (roll over valve in case of an accident), etc.
So, I would recommend trying to get these Technical Service Bulletin issues taken care of first. And you can tell them you have these TSBs and the issue you're having. Especially since the problem might be something where the gas tank has to be taken down to check these valves.

The 1st TSB says "Dealers must perform this Service Campaign on all affected vehicles prior to customer retail delivery and whenever an affected vehicle is in the shop for any maintenance or repair". These are issues that have shown up enough that they put out a Recall or Technical Service Bulletin. I don't think a fuel additive would cause this issue, unless it's something that happened right after you may have added it. Most fuel system cleaners are added with a full tank of gas. Did this happen at some particular time or event? And if so, was it a cleaner you added? With the way this system is designed, it doesn't look like a conventional Evap setup. Like I said though, the diagrams they have posted look different. On the diagram you can see the #3 Fuel Shut off valve looks like a one-way type valve.
I'm reading though that there are a lot of complaints about this same issue with many of these vehicles, and it is saying they do not use a conventional evap system. Some statements say that the filler neck is not wide enough to allow proper air flow. Some say to try turning the gas handle angled to about the 2 o'clock position seems to help with filling. But since there is no vapor line to allow the pressure difference to escape, I can see why there are so many problems with this. If you have a friend who can take a look at it. I would have him/her check the smaller line under where the filler neck is. And see if any air can be pushed through there.
Another thing to check is at the filler port itself, that there is nothing blocking any breather ports at that point.
If the tank has been overfilled, and there is liquid gasoline in the evap canister (which is only made for vapor) that will most definitely cause this problem. But from the amount of complaints, I am seeing on this, it's a design flaw.
Up at the filler neck port is where the air filter is also, checking that for a clogged filter might help too, seeing the number of miles you have on it.