You could use it as a root for another apricot. But beyond that I don't know about other stone fruit as scion. Seedling apricot also usually have decent fruit.

I also have peach volunteer seedings in my yard. It sounded like that peach seeding has more use as root stock for other stone fruits than apricot or plum? how decent fruit a peach seeding bears?
I saw very large white peach in Rome last month. I have never seen peaches in white color before , no any red or yellow color at all, all white. Out of curiosity, I tasted a few, they are very sweet and juicy. I saved some seeds and hope I can grow it here ( in the pot), I am wondering if the fruits quality will be , or close to be the one I ate?

Do you have reason to believe an apricot seed could have fallen or been tossed there?

Olympia,

I assume you mean Rome Italy?

If so, I would encourage you to throw the seeds away. Some strains of Sharka virus (plum pox) can be transmitted through stone fruit seeds.

Europe has long been a hot spot of plum pox, so the risk of infection is real. The last time plum pox was introduced in the U.S. (probably by a fruit hobbiest) it collectively cost stone fruit growers millions. I've personally talked to a grower who was forced to cut down his orchard because he was in a quarantine zone. Anyone in a quarantine zone had to cut down all their stone fruit (commercial and hobbiest alike) whether their trees were infected or not.

A potentially interesting variety is not worth the risk of destroying peoples' livelihoods or hobbies.

There are many excellent white peaches/nectarines here in the states to choose from.

Scott