Billigflug Sold us the wrong flight and now refuses to give a refund

We had to fly for a family emergency and booked a last minute flight through billigflug.de for which we paid €1k+.
However after 4h we realized that there was a mistake. The flight was advertised as having a 1h15m layover in Istanbul but our connection was actually a day later. So in reality, the layover was 1d1h15m. When we realized this, we immediately called them and they refused to accept this. They just said oh it means transfer time from gate to gate but it clearly says on their issued ticket as “stoppzeit”. They said if I wanted to make any changes or cancel my flight I had to pay an extra €100

Eventually we had to pay another extra with the airline at the airport ticket counter to get onto a connecting flight for the same day.

They were extremely rude and totally not helpful. As a passenger what are my rights in this case? Because the website totally sold the wrong thing and now they’re saying they won’t even compensate the change fees from the airline. What can I do?

Edit:
Here is the [pic](https://drive.google.com/file/d/1JD-U9d00EYQvW5b-_AQIprAHQ0xE_kPi/view?usp=drivesdk)
Clearly says stop – 1h15m but onward flight is one day later.