Step kid advice

I’ve been with this girl for almost 4 years. Her kid was 3 when we got together. I need advice on what to do in this situation that happened yesterday because I don’t know what to do. We had gone to a pool we went together and obviously I just wanted to spend time together and play around as a family but the kid kept on going away. (Kid was in a mood that day) Later during the day we got something to eat, once we finished eating I told the kid they were being mean and the kid said “no” which then I replied “yes” and brought up the fact that they don’t want to share whatever snacks,drinks I buy them. The kid replied “do you think you’re my dad” keep in mind the dad did not want anything to do with the kid for almost 4-5 years. He recently came back in to the kids life but doesn’t really check on the kid nor make time to take the kid out, spend time nor buying them whatever they ask for.

I zoned out when the kid said “do you think you’re my dad” and I don’t think the mom said anything about it but I’m not sure since I kinda just sat there with a lot of thoughts running through my mind. I haven’t done anything bad to the kid, I’m always there for them and trying to spend time together as a family spending whatever I can on the kid no matter if I only have $10-$20 left for the week.

I’m thinking about talking to the mom about it in person and just go based of whatever she says about it and what she tells the kid.
What should I do or what do yall think?