Is the hamza in the word "shay'" written on the ya' ("شيء") or separately from it ("شي ء"), and is expiation obligatory for one who swore that it is written on the ya' if that is incorrect?

The word "shay'" (شيء) is written with the hamza on the line, not on the ya' (نبرة الياء). If the questioner meant that its writing with a pen is like its writing on a computer (the hamza on the line), then there is no sin upon him. However, if he meant that the hamza should be elevated above the ya', then he is mistaken, and it is most likely that no expiation is required for this oath, because it is an oath of inadvertence (yameen laghw), which is when a person swears based on a strong assumption and then it turns out to be otherwise.