Gas Tank

I have trouble pumping gas at one specific gas station. When I pump (either holding the nozzle or putting the latch on so I don't have to hold it), it stutters and dispenses about.00001 gallons of gas at a time. Sometimes I go to a second pump and it works, sometimes it happens again.

Another customer saw what was happening and told me there was something wrong with my gas tank. I don't think there is given that I have successfully pumped gas at several other gas stations (even those of the same brand).

Is this an issue with my car or an issue with the gas station? The gas station has only been there about six months.