You'd be better off calling a family lawyer and seeing what they have to say---the laws vary according to each state. I would think that unless your husband stipulates in his will or on the bank account that he wants that child or that woman as the beneficiary then they have no legal claim to the money or any of the assets. I suggest you make him pay child support though because the state will bitch slap the hell out of him when the catch up to him if he doesn't pay child support (the interest is a killer and then he'll be working just to make the child support payment). If you have a joint checking account, I'd separate myself from that and start keeping your money apart from his so that your money isn't going out the door to that other woman and child, and I'd also be sure to take my name off anything else that you have jointly. Same with tax returns--don't file jointly with him because it might screw you if he's not paying child support (the government just might decide to hand that over to her too). Good luck, and call the family lawyer and check out your state laws.
You definitely need to write wills, both of you. In most states, if you don't have a will, and your husband dies first and his estate passes by intestacy, the child will get a share of the estate.
I agree with the previous pose: you need to see a lawyer, but better to go to an estate planning attorney than a family lawyer. You need to find out if your state is a community property state, and you need to draft a will or some trusts to ensure that your property will pass in the manner you want it to when you or your husband die.
Why are you still hanging with this cheater. Shake him with a divorce and sue him with alimony and child-support,assuming you have children. I would suggest counseling and work on your self-esteem and self-respect.
Think carefully before you cut this child out of your husband's will. Don't blame the child for the mistake its parents' made. My mother forced my dad to cut my half-brother out of his will. It put a greater strain on their marriage than discovering the affait did. After Dad died, his ex-mistress never bad mouthed Mom, but the word got out anyway and everyone in our community thought Mom was a bitch. My brother grew up poor, but got a scholarship and went first to college, then medical school. Now he's our town doctor and Mom is so embarassed that she travels two hours to go to another doctor rather than face him.
Your Mother did what she had to do then. I can not say she is/was a "bitch". It is bad enough when a woman know and willing date a married man,(we are all entitled to mistakes) but to get preg. is a stupid, stupid thing. Women that do that make a decision and they are the ones that are punishing their own child for the mistake she and the cheating father did.
A wife that brings home half the bacon, has a right to make sure any kids she met her husband with before and her Kids get what they are entitled too, not an outside adulterer's child. Child soppurt and that is it, noyhing else!!! Remember if or when the father/husband dies, whatever the child get they will share with their Mother in the long run... (The thiefing woman that almost tore your family apart).
Men are half resposible, however, Men don't get preg. or make decisions to have or keep babies. Women protect yourself, why bring another innocent person in this world with YOUR shame.