You have no evidence of your boyfriend's interest in you or your daughter. He says he wants to marry you (if that's what you mean by he "claims to marry") and that he loves your daughter, but he's just on the take for bus fare? Do you have (or does he think you have) such a good job that you can support yourself, your daughter, and him? I'm not sure why you think a boyfriend should support you and your daughter though. She is your responsibility since you took custody of her. You don't say why you took her or if that was sanctioned by the court, so it's hard to know what her birth father's role is here. Why wouldn't he be required to provide half of her support?
You also don't why she was with her father and being raised by him until you stepped in, but I would imagine that she's got a lot of issues in being removed from one situation and put in another, and then having another man introduced into her life who is not her father or your live-in husband. So, really, your situation doesn't sound too stable (financially or emotionally) to introduce another significant variable - a boyfriend with questionable dedication.
You're new to Mamapedia so we don't know anything about you - so more details would be great. Without editing your original question, can you add to it (write "added" at the end and put more details, or put something in the "So What Happened" section) to add essential information?
Are you in the US? Your profile says CA but a lot of people disguise their whereabouts. The reason I ask is that you use some very unusual phrasing, particularly for someone who went to college. You say things like "I had her with another man whom we broke up while in college" and "I had another boyfriend whom we are engaged to be married" and "the salary is little." These are not proper American English for a college student/graduate, so I wonder if you are in another country where the custody and child support laws may be different. If so, you have to take our advice with a grain of salt because it may not apply where you are.
However, that aside, I'd ditch the boyfriend since you and your daughter are a package deal, and I'd work out an enforceable, legal support agreement with her father. I'd also get counseling to help set goals (financial and other), figure out why you choose inappropriate men, and to help your daughter with the massive adjustment in her life and living situation.