The two previous answers are correct. You cannot say he's a three-children father. However you can say this though in many ways: He's a father of three children. He's a father of three. (Children isn't need as the word Father already implies children) He has three children. Or you can replace Children with Kids. Kids and Children are both common words used in the USA.

He is the father of three children.

No. I know what you mean but it is not correct. It's better to say "He's the father of three."

I think you are trying to make it similar to when we say "He's a one-woman guy," meaning he only goes for one woman at a time. In that case I think it would be "He's a three-kid guy" would make sense, but it would mean he is the type to want or have only 3 kids and that's it. But to say he's the father to 3 children, I wouldn't say it.