Prunus persica (Peach tree) is only hardy to about zone 7, so not much chance outside in Ohio. I don't know about this species, but most Prunus require several months cold stratification, and often several months warm stratification first.

Your best bet is to sow now and leave the pot outside to expect germination in spring. Before you sow, clean the seed thoroughly, then soak overnight in fresh water to remove all traces of the pulp.

If these are hybrids then you will have problems with the results. They won't resemble what you saved the seeds from. Seed saving is generally done if you grew a non-hybrid (open-pollenated) variety yourself.

Most peaches and other fruit trees are generally grown by grafting the desired variety onto a different tree which is less vulnerable to diseases and grows better in your climate. They grow one kind of tree, cut it off about 3 inches above the ground, and then grow a peach tree, cut off the roots, and graft the two together. You might have fantastic results with planting a peach pit, I don't know.

I live in central Texas and I have some fruit that I have eaten and saved the seed. I would like to know when to plant them. I have a peach,purple plum and a large apricot.
Thanks,
Kaye