Question about patrilineal descent in terms of converting

Hello everyone,

I have a non Jewish mother and a Jewish father, and am interested in an orthodox conversion. I understand that this does not make me Jewish, however I have heard that it is sometimes slightly easier for zera yisrael to convert? In reality, is this actually true? Does this only apply to those who were raised with Jewish traditions and therefore have prior knowledge of Judaism? Also, would I be required to prove that I have a Jewish father? If so, how would I prove this? My father was raised secular so I don’t really have records to prove that he is Jewish, only stuff from his parents. Thank you, and my apologies if this is too many questions.