The Jewishness of George and Ira Gershwin, children of immigrants to New York, is widely known and always included in their biographies, but I've actually found nothing indicating that they recognized direct Jewish influence or inspiration for their music. There's a lot of speculation -- does the start of Rhapsody in Blue or the wailing note of Summertime reflect a Jewish musical echo? But no hard evidence.
I found one indication that George Gershwin was conscious of a Jewish identity. Here's a quote from a letter he wrote in 1936: "Of course, there are depressing moments too, when talk of Hitler and his gang creep into the conversation. For some reason or other the feeling out here [in California] is even more acute than in the East." -- from Jewish Theater.