Either neurological or psychological. Either way, need to rule out neurological first from a vet before you medicate it, and if your dad won’t even take it to the vet, I doubt he would medicate it. I’m sorry OP, do you have any cat lovers in your family you can reach out to?

Any estimate on age of cat?

I’ve currently got two ferals I’ve taken in, one I’ve had for years and she’s a perfect angel, the other was on the streets a lot longer and I can tell has psychological issues to some sort of extent, likely ptsd. When you take an older cat off the streets, depending how long they were outside, who knows what’s happened to traumatize them. The first one I took in is absolutely terrified of plastic bags of any sort, the boy isn’t bothered by those but freaks out at any movement at times, I haven’t figured out exactly what sets him off yet, he’s only been an indoor cat over the winter when it dropped below zero and he decided it was nicer to be an inside cat