Sometimes, but not reliably in every case. A JPEG may include metadata such as the EXIF/XMP Software tag, which can show that Photoshop was the last program to save the file. Many photo management tools can search or display this tag.

However, metadata is not dependable proof: it can be removed, changed, or omitted entirely. For example, export methods such as “Save for Web” may strip metadata unless those options are enabled.

If metadata is missing, the only option is image forensics, such as error level analysis (ELA) and related techniques. These tools analyze the image data itself for signs of manipulation. Even then, they may only suggest that an image was altered; they do not reliably prove that Photoshop specifically was used.

So the short answer is: check the metadata first, but if it has been stripped or edited, there is no guaranteed way to identify Photoshop as the editor from the JPEG alone.