It would be good if you could get that in writing, discreetly. Not from your daughter. Maybe send your ex a message along the lines of
"Hi. I am concerned that daughter is referring to me as her stepdad and seems to believe that your boyfriend is her "real Dad". Please can you confirm that you will correct her understanding of who is her biological Father (real Dad) and who is her Stepdad and what this means? Thank you."
Just by sending that message, whether she replies or not, you have evidence of what ex is doing.
Having said that, if your ex is an alienator she might react badly. So if you think it might impact on your daughter, sending a message like that, then you could just put in a position statement that you're concerned by this (although it's not much different in terms of how ex would react). And meanwhile explain to your daughter that this is incorrect. How old is she? My son was about 5 when I had stuff like this. I explained to him that I was his real Dad/biological Dad and Mummy's husband was his stepdad. He argued back and said no it must be right because Mummy told me. So I said well Mummy must have made a mistake (you can't criticize ex to them or accuse her of lying or they'll resent you). He was absolutely insistent that Mummy was right. In the end I showed him his birth certificate. He said - so you are my real Dad. It was hard. He then had to cope with the idea that Mummy hadn't told him the truth. He didn't say anything.