@awkhumalo,
Then respect her wishes.
About all you can do is ask her to write a letter to be sealed and given to you to read after her death.
Note: if she is that set against telling you anything, then your father is likely to be: dead, married to someone else at the time of your conception, a gay man who had a fling, a relative of hers, in jail, in a mental institution, a rapist, one of several guys during a group sex encounter, or one of a string of one-night stands (and she may or may not be sure which guy he is).
Of course he could also be someone of power where this would be a huge embarrassment. But the truth is, that's far less likely than the other scenarios I've outlined above.
People don't keep these sorts of secrets quite so closely unless they have a damned good reason to do so.