Where should I start with researching my Italian father’s family history?

I was born and live in the united states. From what I’ve been told, my biological father was born in Italy. He hasn’t been apart of my life and I haven’t seen him in 34 years, so I can’t ask him.

I was never sure if that was the truth because from what I knew of him, he wasn’t exactly a good guy so lying about where you were from in the 80s when you couldn’t fact check anyone didn’t seem like a stretch.

I have a document somewhere from when I was born where he signed it and he listed where he was from or born. He wrote San Vito Java, Italy. For years I could never find anything about that town. I figured it was a village or something that got incorporated with a larger city.

I recently took a genetics test that also provided Ancestry results. To no surprise, I’m 71% European and notably 10.2% Southeastern Europe and 4.4% Sardinian.

When looking for my father’s birth place, I never considered the islands. I searched San Vito Sardinia Italy and there it was. It’s on the south east side of the island about an hour from Cagliari.

This feels like a thread I should pull on. I’m looking for help on how I can learn more about my family history.

Any help would be greatly appreciated.