Well for one he will have to prove that he is the father through a dna test because he never signed the birth certificate. so thats in your favor right now.
two just giving you extra money here and there doesn't actually mean a thing. there is not actual proof that he has given you anything so it doesn't count as child support. thats something that only the government has control of and they are only the ones that can record that. if you really want to prove that you pay for everything for your daughter save all of your reciepts and that will be enough to prove it.
now back to custody. like i said he will have to pay himself for a dna test if he chooses to take you to court. thats alot of money to put out but because he would be the one taking you to court it would have to come out of his pocket. now if child support stepped in to prove that he is the father they will pay for one test and that would be enough proof for him to take you to court. but as it sounds right now he has absolutely no parental rights because his name is nowhere on the birth certificate. usually they will demand paternity to be proven and if its proven they will award the mother with full parental rights and give the father visitation rights. in some cases its joint custody but thats more if you guys were ever legally married with paperwork to prove it. most normal circumstances the father will never be given full custody by a court. its usually very special circumstances that that happens. and being that he hasnt been around much they are going to probably want him to go to parenting classes and possibly therapy.
i would call lawyers for free consultations some of them do that and ask their opinions. otherwise the court might appoint you a lawyer but i am not sure fully about that. what will happen is they will have to prove who if fit to be a parent and most likely there will be visits. but if you have a lawyer even if you dont have the money its reccomended that you get one. they will be able to negotiate the visits for you among other things. and if you push hard enough you will get what you want most likely. fact of the matter is she is still very young so sending her out of state would most likely be out of the question. but keep in mind that right now he has no rights what so ever because he isnt on that birth certificate. until they prove he is the father he can't do anything.
so if i was you i guess i would make a choice on wether you actually want to move forward with child support and prove he is the father or wether you want to just raise this baby by yourself on your own without him being involved ever. yes that is the harder road but sometimes its the best. best advice to give is that you need to keep a log of everything. money he gives you, phone calls, visits, conversations, what they are about times dates everything. i wish you luck and if you have any more questions please feel free to message meand i'll try to answer anything best as i can. but i am not a professional by any means i have just been through a very similar situation so i know.