Fiance might have another daughter?

So my fiance might have another daughter.. When I met him he told me about her but said she might not be his.. she would of been only like 4 months old at the time. Since then we now have 2 boys a almost 3 yr old and a 6 month old.. Knowing if this girl is his is on our mind off and on.. cause you wonder if the boys have a sister or not. The mother used to always say he was the father and she knew it but they werent dating at the time and it was a one night thing. They used to bicker about it alot when we first met. however now we dont talk to her unless its on facebook and its never about him being the daughters dad its about other things or we will share things about our kids since they are the same age. The little girl has a dad that has been there for her before she was born not sure if he adopted her or not but thats who she calls daddy. Well we were wondering if my fiance should ask for a paternity test just for ease of mind.. But then he might have to pay child support which we are already living almost paycheck to paycheck. If it was hers the only way we would pay child support is if we got rights to her right? If she wont let us see her we wouldnt have to pay? Idk if we should do this paternity test or not.. my mom says its opening a can of worms that doesnt need to be opened and will bring more people and problems in our life.