Dear Mr. Smith,
Thank you for posting your request on History Hub!
Most photos during the Korean War Era were not normally maintained. There may be a chance that there’s a photo of your father in his military personal file which is located at the National Personnel Records Center in St. Louis. You can request his military personnel file online at: https://www.archives.gov/veterans/military-service-records. You also can contact the National Archives Still Photo Branch to see what that section can do for your search. The Still Photo Branch email is: firstname.lastname@example.org.
We hope this is helpful. Best of luck with your research!