Sorry you have had this to contend with when you are feeling so vulnerable.
Get the maintenance sorted out.
Unfortunately, very little is on your hands. The other woman, whatever her reaction to this man, may not ever wish to have contact with you or for her children to know your child, and there is nothing you can do about that.
He has put himself in a position where he can not actually do fully right by anyone in his life. And you are feeling the fall out from that.
The 'secret' isn't sustainable in the long run, as your child grows, and if (when) she finds out, she will be shocked, feel betrayed and hate him. His other children, likewise. What will happen at Christmas, birthdays? With his little lies to get away. HIding his phone in case your child contacts him...Whatever you tell your child, (and you will have to lie unless you say 'your Dad is with his other family') they will be second priority.
He is panicking about the situation he has got himself (and everyone else around him) into, and being unrealistic. I think you have to have a firm clear conversation with him, and if he really cannot tell his partner what is going on, you need to get your maintenance on place and create a big distance.
And as others say, don't use his surname. So many posters on MN regret this, when they have subsequent children, when they travel abroad with an absent Dad. Why should YOUR child , brought up by YOU, have the man's surname?