I had a baby today and have no feelings for it
Why would you have no feelings about your own baby?
I don't see the child as mine.
I'm sorry you might think you're not paternally related to it, but they are still your child and they see you as their father. You can't rob such a new life of that privilege.
Me being involved in the child's creation doesn't make me part of its life. I can't be held responsible for something that I don't want.
If you helped create the baby, then you are a part of it's life and there is a duty to care for that child. Growing up without a father would be a terrible thing to put on your child.