If I have saved an image in JPG format after doing some edits, is there a way to identify that it is edited with Photoshop?
it depends what you're looking for.
1) File Meta-info: the meta information contained within the file can reveal which s/w saved the photo last (with possible edits). But this can easily be changed afterwards or deleted by another s/w.
2) Image data: now, if you're looking to find out if a photo file has been tempered (edits made to it), you should look into Error Level Analysis and photo forensics.
It's easу. Photoshop CAN write its name into the EXIF Software tag, so you can locate images that have been edited by Photoshop using any photo management program that can locate images by the EXIF Software tag:
However, if you save your images as JPEG using File > Save for Web option (Ctrl + Shift + Alt + S) make sure that you checked the option below:
otherwise you will not be able to identify your images later by EXIF/XMP Software tags.