I think the best thing is to see a psychiatrist if there is genuine concern. As SP says it is often family members who notice a difference.

Schizophrenia classically goes through a "prodromal" phase, which may start out like depression, or may just be trouble sleeping before things start getting strange. It can also come on suddenly though, so hard to tell.

I think the thing most people might pick up on themselves is hallucinations. That could be as simple as hearing vague noises, or could be voices or seeing things that aren't there.

If you aren't aware, even if your Dad has schizophrenia... you only have a ~10% chance of developing it, so it's far from a given you will get it even if it common in your family.

I don't have schizophrenia, but it was the voices that alerted me to my psychosis after I asked my Mum if she could hear them & she said no.