Thank you for your advice, a mutual friend told me late september, she also set her ultrasound picture as her cover photo on facebook and in the comments of everyone congratulating, her exact reply to the comments were "thanks everyone its a girl due late september, early october". when i spoke to her on the phone when i called her, she was vague and only said "my first scan said i was due the 1st week of october, but its okay it is now mid october" by the sound in her voice it sounded like she was worried but trying to keep a brave front.I tried to keep it short and sweet and not put any pressure on her.
If she is telling you that you are 100% not the father, it does sound like she believes it from the evidence, not that she is fearful that you will push for custody. In such a case, she might find you pesty if you keep pushing her and be annoyed that you aren't believing what she says. This will not get you the information you would like so you can put the whole concern behind you.
If you have not been too much of a pest so far about it and she is still speaking to you, I would suggest you ask if she would give you a copy of the report from the very first ultrasound she had. (That is, the report that includes the date of the ultrasound, the gestational age of the pregnancy measured from the assumed first day of the last menstrual period, and the estimated due date.) Put it on yourself, say you are just a nervous sort of guy and want to be entirely sure of everything. Maybe she will send it to you if you put it like that.
The real reason you would like to see the actual report is simply because usually the doctor crisply says a due date, not a loosely-identified bracket of time. (Or was the "around the end of September/early October" language yours and she actually said a particular date? If so, what exact date was it?) The report should say an EDD. From that, you can use a conception calculator and work backwards 266 days or so, to see if there is even a chance you're the dad.
Yes, docs might adjust the projected due date as the pregnancy progresses, but the earliest ultrasounds are the most accurate for the purposes of dating the pregnancy. Later changes merely reflect the fact that babies grow at different rates.
My suggestion is to ask the mother, not the daughter, if her daughter did in fact have an early ultrasound. Explain that if the ultrasound really was in the fifteenth week or earlier, and if it indicates a due date of around October 1, then you could possibly be in the picture, and so you want to see a copy. If they cannot cough one up, or won't, frankly, you should just let it go. There is nothing to gain from turning into a basket case now over this. (And a lot to lose, if you have a nice girlfriend and won't shut up about this.)
It sounds less likely that your friend is afraid you will try to take away the child than that she is sure you really are not the dad. Try to trust that. Even though she is emotionally unreliable, it does not sound like you say she is too stupid to listen to her doctor and hear what he is saying about dates. Women take this kind of thing dead seriously even if they have other issues in their lives. When the baby is born, you can talk to an attorney about getting a court-ordered paternity test, to put the entire matter to rest.
In the meantime, don't tie yourself into knots. Usually when a woman is pregnant and thinks there is even a chance that someone is the dad, she will call him and tell him that he probably is, not that he isn't. Don't bug her or her mother, don't obsess, don't over-dramatize, don't catastrophize. Time will answer this one.