Not sure if this will do what you want, but Login Items on the Mac is equivalent to Startup Folder on Windows.

Apple menu -> System Preferences -> Users & Groups

On the left is a list of user accounts, click on yours.

On the top-right are 2 tabs, Password and Login Items. Click on Login Items.

Toward the bottom you'll see a + and -, click on the + then find jEdit with the file dialog.

Might need to check Hide so it starts up hidden, don't know.