When I was pregnant the father of the baby didn't get involved at all. All the things for the baby I had to buy myself, therefore I told him I don't want him to be anywhere near the baby, because he's not worth it and I didintt get any support from him, but after the baby was born I decided to give him a chance, an opportunity to see the baby and to look after her. The baby is 1 month old now and in that period he only visited her once at home and twice at the hospital, plus I still don't get any financial suport from him, so I want to go to court to get the financial help from him, so if I go, what about court expenses will I have to pay for them or he has to?

You may be able to get him to pay expenses. But the filing costs will be minimal. Check with your local court as they vary.

Do you know about how much those minmal costs for me would be?

No, because I don't have a clue where you are. Court costs and filing fees are very local. Generally set on a county level, but may even be set lower than that.

Your best bet is, as I said, to go to the local court for a fee schedule. You may even be able to find it online as many county governments have WEB sites these days.