Seriously, if you want to, take the suicide option. Your daughter that you do claim and your new child you just found out about will both be eligible for social security death benefits. Your current girlfriend won't be having that family you with you are so looking forward to, assuming, of course that it really really counts if you really really LOVE the mother of those children, as far as what support they need from you. And of course you'll be out of it all, no longer anguishing over your past mistakes, the pain, the dashing of your hopes.
Yes, we've all made mistakes. And sometimes those mistakes preclude other things we really wanted in life. Sometimes you cannot unbreak the egg, cannot change reality, no matter how much you would like to start all over again with a new woman and have new children where your family dynamic can work out perfectly. So you always have the option to kill yourself because you cannot accept that.
You made choices several years ago which left new human beings in the world who need support. It sounds as though you've been available for your one daughter, have been supporting her emotionally as well as financially. Kill yourself now and end that support. Set her a wonderful example of how dads act, how people cope with adversity, what to do when things don't work out as you've planned. Is she emotionally in a situation where she doesn't need you anymore? Great.
The child you've not had anything to do with before? You still created this person. You still have to pay. That's the law, and that will happen, dead or alive. This could be a wonderful opportunity for you to get to know and love another deserving child. You and your girlfriend could adopt the larger attitude, and give some love to this child, instead of saving it all for your "real" children that you're going to have together. If she's not on board for this, her interest in you was mostly material anyhow, and it's good you found it out before you had any more children or wasted any more time with her.