I would encourage the idea that she has only one dad, and she has a step-dad who also loves her very much. I would also encourage the idea that we can have many people in our lives who love us and whom we love and that it doesn't mean that we love anyone any less. That's an important lesson for all kids.
The thing is that if her dad is jealous, it is going to bite you and your fiance in the butt the most. If your daughter is feeling like she has to choose between her daddy and another guy who is trying to replace her daddy, she is going to choose her dad and resist the enemy trying to replace him. So, make it as easy as possible for her to love her dad with all her heart. Your fiance can consistently meet her needs and provide love to her, and she'll come around to trusting him. Acknowledge to her that he isn't her dad, but that he is someone who loves her and cares for her. That way she doesn't have to see it as him trying to replace her dad, which sounds like a fear that her dad has as well.
At three, she's too young to really understand, especially all the adult emotions, hurts, jealousies and fears that go with this situation. Your fiance is going to have to develop a much thicker skin if he's finding a three year old's actions to be that hurtful. His job is to make it easier for her, not harder, which means that whatever hurt he is feeling needs to be set aside right now.
When I was adopting a toddler, one of the most helpful pieces of advice was to make a plan of things that I would do for myself to take care of my emotional needs because it would be a long time before my child could/would show any form of gratitude or be able to validate my emotional needs. Even though I was providing a whole wonderful new life for her, she would be sad, full of grief, angry, and hard to deal with for an indefinite period, and I needed to plan for another source of validation of parenting and a plan on where to get emotional support. I think that the same situation applies for your fiance...your daughter isn't going to appreciate him just hecause he's been in her life, especially when his being in her life is creating some stress and anxiety with her daddy. In her world, your fiance is bringing in some baggage that is causing her to be sad, angry and to grieve not having her dad all the time. She's not going to say "thank you" for a very long time; don't add the lack of gratitude to her burden. If your fiance can love her unconditionally and help lighten her burden, it will come in time.