If your father is this childs father he had a moral duty to provide for him/her in his will unless he discharged that duty during his life. If he fails to do so the child (acting through the mother in this case) can make a claim under Section 117 of the Succession Act, 1965. That's a difficult case to mount, but I'm guessing that if the case is taken it might cause some embarassment.
However, there is no obligation on you to provide the financial information requested at this point. The will will be public record when it has gone through probate, but the rest of the information is none of her business. To me it sounds like she is trying to assess how much the estate is worth before offering to take X amount to "go away". My immediate instinct would be to say that there will be no discussion of the estate until paternity is proved.