No. You should have legitimated the child and asked for custody/visitation in the same proceedings. In any event, now, you have to file for custody/visitation. The good thing about just legitimating the child is that the court looks at the best interest of the child. The court looks at several enumerated factors to determine who should have custody or whether custody should be shared.
Regardiess, you should move forward and file for custody as soon as possible.
A fit father who legitimizes his child and also petitions the court for custody and visitation will almost always be granted joint legal custody and the customary noncustodial visitation in the county where the divorce is filed unless the other party is able to show the Judge that they are unfit. In order for the noncustodial parent to get joint legal and physical custody, most Judges will only grant it if both parents agree to it and even then some Judges will not award it. If he and the mother get along and file a joint parenting plan with the court asking for joint physical custody then he stands a good chance of getting it but he might have to seek some guidance from the Court as to the form of joint custody that the Judge will approve. But if the mother does not want joint physical custody then his chances of getting it are low since it is hard to make joint custody work when parents get along but it is almost impossible if they do not which is why most Judges do not attempt forced court ordered joint custody.