Before sleeping I watched time for fajr it was 4:42 am, I woke up ate and drink something stop before 4:42 than I checked timing again on Salah.com and it was showing time for fajr 4:44am so I drink a sip of water than I realized time from Salah.com was from Muslim World League while 4:42 timing was from Islamic University at Karachi so is my fast valid or it is gone?
First of all your post lacks some necessary information to answer it correctly, so you could conclude your answer from the following:
You should know if you know the ruling and you despite this knowledge ignore it, then you are committing a sin, as this is a part of kufr (rejecting an order a ruling of Allah's shari'a the more you do it without necessity or intenionally the closer to kufr it is). Hence your fast would be invalid and you should repent!
Allah the Almighty says about such people:
But if they do not respond to you - then know that they only follow their [own] desires. And who is more astray than one who follows his desire without guidance from Allah ? Indeed, Allah does not guide the wrongdoing people. (28:50)
... They follow not except assumption and what [their] souls desire, and there has already come to them from their Lord guidance. (53:23)
On the other hand Allah recommends us to follow his orders and those of his Messenger saying:
Say, [O Muhammad], "If you should love Allah , then follow me, [so] Allah will love you and forgive you your sins. And Allah is Forgiving and Merciful." (3:31)
Say, "This is my way; I invite to Allah with insight, I and those who follow me. And exalted is Allah ; and I am not of those who associate others with Him." (12:108)
We are asked to follow the orders of Allah by verses such as:
Say, "O mankind, the truth has come to you from your Lord, so whoever is guided is only guided for [the benefit of] his soul, and whoever goes astray only goes astray [in violation] against it. And I am not over you a manager." (10:108)
... . Legislation is not but for Allah . He has commanded that you worship not except Him. That is the correct religion, but most of the people do not know. (12:40)
As Allah is the most just:
Is not Allah the most just of judges? (95:8)
But if you by fault or erroneously or due to lack of knowledge ignored that ruling you might be forgiven. Therefore in such a case your fast would be valid. Due to verses such as:
... And there is no blame upon you for that in which you have erred but [only for] what your hearts intended. And ever is Allah Forgiving and Merciful. (33:5)
and ahadith such as:
Allah has forgiven for me my nation their mistakes and forgetfulness, and what they are forced to do." (Sunan ibn Majah)
In your former post Different Fajr prayer time which one to follow? you have asked about the prayer times and have been informed about the most correct calculation in your place. If you trust these answers (and have cleared any doubt about that) you should accept and follow them else you'll be sinning and you should repent. If due to a mistake you've chosen the wrong calculation (the correctness of such a calculation might have a certain margin of 1-2 min at maximum) or you haven't intentionally chosen a more comfortable one your fast would be valid, else you have starved for nothing, as your deed was half complete. As an advice: note that for fasting Ramadan correctly it is necessary to believe that it is ordered and without any worldly intention like showing off based on ahadith like this in sahih al-Bukhari, beside this one should try to be kind and do good deeds as ever, else fasting has no meaning as quoted in this hadith states.
Once you know of your error repentance is appropriate!
Valid, because you used one of the calculation methods, so it was as if you had nothing to do with the other method because you planned using the other.