Blue Jays are omnivores, meaning they eat a variety of foods. At feeders, they eat sunflower seeds, whole kernel corn, suet/suet mixes, and peanut butter mixes. When I lived in NY State, I wouldn't feed peanuts because of the price and I had Blue Jays all year round just by putting out sunflower, suet and peanut butter mixes.

I have a bird table/tray (platform on pole, screened to allow rain to pass through). In addition to a few seeds, I often put out (cut up) pieces of poultry skin and fat, fish skin, gristle, cartilage, fruit, older nuts and seeds, and sometimes bread. I have a baffle on the pole to keep rodents away. Sometimes I put out older butter or peanut butter. On the few occasions when I cook a ham or lamb, I freeze/save that fat (cut up) then later on make a melted, reconstituted "fat/suet block" that I put into a large hanging cage (in cold winter). The fat cage hangs from a tree about 40 feet from the house but in view of the window. The small birds can fit through the wire mesh, the woodpeckers can access the fat block from the outside of the cage. The jays can pick up what falls.