What can I do to get my name placed on the birth certificate and get visitation rights to my daughter when the mother won't let me

Child support goes along with that until they are 18 and some places, 21 and college tuition.

You have to bring a paternity suit and prove parenthood, then petition the court for visitation, and have them set a schedule the mother will HAVE to follow.

What can I do to get my name placed on the birth certificate and get visitation rights to my daughter when the mother won't let me

You have to go to court and request that the court order a paternity test and, based on the result, declare you the legal father. At the same time, you can request visitation rights.

The mother can, counter file for child support.

I would strongly suggest that you get an attorney for this. If the mother is going to fight you, especially if she has legal representation, you will need your own.

File for visitation. If there is any question then ask the courts to mandate a dna test to prove you are the father. After that is over with then you can go to the hall of records for your area and have the birth cetificate amended and your name put on it.

As noted, you will have to file suit. Your name on the birth certificate will, as such, get you few if any rights at all.