Bill,
The missing patch pretains to father's first squadron. He got his wings in 1955 and was immediately attached to attack squadron VA-55. They were better known as the Warhorses. During his three years with the squadron they flew two different aircraft. The first was the AD-4 Skyraider or as he called it "The Spad". Later they got an updated version or AD-6. Thereafter, the squadron transitioned to jets with the FJ-4 Fury.
In those years the squadron was attached to NAS Miramar. He also did two carrier deployments, the first aboard the USS Hancock flying Skyraiders and the final deployment abourd the USS Bennington flying the FJ-4 Fury. His time with the Warhorses can be chronicled in the website set up by the A-4 Association
http://www.skyhawk.org/3e/va55/va55.htm.
By using both the squadron's information available through the website and contacting and taliking to the surviving squadron members has given me good insite as to the probable patch it would have been. None of the squadron members remember this particular patch. Notwithstanding, the only patch on dad's original jacket and shown on the website is the Hancock ATG-2 1957 cruise patch.
Unlike the Airforce, and until fairly recently the United States Navy allowed many different types of patches to be attached to an individual's jacket. In short, during my father's entire naval aviation career, within reason, there never were any rules or codes governing how or what they could display on these personalized jackets. Normally ,these older jackets did have patches attached that could include Carriers, Air Wings, Air Stations, Cruises, Squadron, and or the different types of aircraft flown by the individual during their aviation career. The vast amount of the different insignias worn by the aviation personnel in it's self compounds the ability for identification of those aviation related patches. In addition, I have found that many patches were conjured up at the squadron level and many of these patches would inevitably vary with each new tour. It is simply difficult to identify many of the older naval patches as they went undocumented from the beginning.
Dave