Not sure if it's true, but according to my history class antisemitic laws designed to punish Jews for killing Jesus existed as far back as the middle ages. One most important to shaping modern hatred was the prohibition of Jews owning property. This meant that Jews could be neither peasant farmer nor nobility and channeled the ethnicity as a whole into middle class professions, especially law, banking, and tax collecting. This restriction meant eventually that debt was generally Christian majority owing Jewish minority money and prejudice grew even deeper from there.

I would recommend checking out the FAQ as this question is a common one- for good reason! Here is a question I answered a while back which covers this and includes the origins of some typical antisemitic canards.

Basically, in the majority of societies they have lived in, Jews have been a minority, and that has made them the Other, which has made them hated. And hate breeds even more hate so it's kind of a cycle, with antisemitism breeding antisemitism because if it seems to have always existed, that means it must be right, right? Etc. Antisemitism is particularly well known because Jews have been a minority in so many places, and also because Jewish cultures have survived and even thrived despite the antisemitism prevalent in the West, creating a strong Jewish identity, unlike, for example, with the Cagots of France and Spain, who's identity has disappeared.