I have a partner were living together for 6 years, suddenly ww have misunderstanding and he needs to be far away from me, mduring that time he accidentally have a child but he did acknowledge the as his daughter but her parent accept that child.. if ever the mother will file for a case is there chance to win the case that he will file if ever like a support for her child, can we win the case?

First he does not accidentally have a child, he did not trip and fall naked on top of her.

You two were broke up and he slept with at least this one person and they have a child.

Does not matter if he wants to acknowledge the child or not, at least in the US, all she has to do is file for child support and ask and demand though the court for a DNA test.
Then he will have to pay child support, there is no way, assuming it is his child proven though the DNA test that he will get out of support.

He can ask for visitation if he wants to.