When a married woman becomes pregnant and gives birth, the husband of the woman is automatically considered to be the father by law.
This is not questioned unless he has doubts and wishes to establish paternity at some point, or someone else believes they are the father and wishes to establish paternity.
This can still be settled out of court at this point if you and the mother are willing to sign an affidavit stating that you are the father.
But there is another player in this situation - the husband.
He has to be willing to sign an affidavit as well stating you are the father.
This may not happen.
To begin with, many women are not even going to admit they had an affair and, if the husband is willing to raise the child, he may not be willing to sign.
At that point, you would have to go to court to establish paternity and most likely request to have some type of testing done as proof.
Dealing with paternity issues when the woman is married can be difficult to deal with.
Even if she is married and well taken care of, you will be required to pay child support.
  You can get visitation rights and possibly joint custody in any paternity case, but one such as this can make it harder.
If you believe you are the father of a child with a woman who is married, make sure you are clear on what you want to do and what your goals are as far as your rights as a father.