My gut instinct.
There's something going on. Your daughter has a problem, which she feels only a "real" dad would solve. It's strange that after four years of not seeing her biological father, she is now crying every day. Perhaps she feels she cannot confide in you, so the crying is a manifestation of her frustration.
Is your rapport with your partner a happy one? Are there are any fights? Do you spend time together, alone, and have fun? Do you go out together as a family? Does she feel accepted by your partner's parents?
Have a chat with her teachers, find out how she's doing at school. Does she have friends? Is she popular? Tell her teachers that your daughter has been acting moody at home recently (no need to tell them the whole history if they don't know already) and you're wondering what the cause might be.
You don't mention if she has any half-siblings. If there are any, ask them if your daughter has talked to them about her biological father.
If the problem is her biological father's absence in her life, consider whether visiting her paternal grandparents might be a way to fill that "void". Has she ever seen seen her paternal grandparents? Were you on good terms? Have you stayed in contact? Perhaps now is the time for your daughter to build a rapport with them. If, for whatever reason, you feel this might jeopardize your daughter's safety or emotional well-being then leave well alone.
Spend some time alone with your daughter, helping her out with homework, or doing the shopping and ask her what's bothering her. If she replies she misses her dad, ask why she needs to see him so badly. Listen to what she tells you, above all she must be able to talk about her dad without any interruption. Encourage her to open up without passing any judgement, be as neutral as possible. Here I am in agreement with
Francine DeGrood Taylor's advice: “I would start by making certain that she knows it wasn't her fault.” So reassure her she is loveable, beautiful and cherished by everyone in your family.
You might discover what triggered this anxiety, which I think is the key to this problem.