Blue Jays can be quite exasperating to photograph. They are quick, smart, skittish and extremely agile. But they have one weakness, an insatiable appetite for unsalted peanuts. Blue Jays are pretty common, and they will come to check out anything new in their area, but getting one to come close enough to the camera for a good shot requires some kind of hide, which won't fool a Blue Jay, or bait. They will eat sunflower seeds and other bird seed mixes and corn, but they love peanuts and will soon come close enough to steal them for as long as you want to keep putting them out.
In a local county Park, someone years ago put up a few bird feeder stands near a road. Over the years, enough people have found it and come by often enough to stock it with seed that many of our native and migratory birds know about it and will visit it all year around. Blue Jays stay here year round. I will jam a penut into a crack in the bark of a tree, or anything I can find that will hold it and make them work to get it. They seem to get into the game and even like to find hidden peanuts. Nearby branches are a plus, as they will always land nearby and check things out before going to the peanuts. This is where you aim the camera, or at the place the peanut is, and if it takes a few seconds to work the peanut lose, you can get quite a few interesting shots and more natural shots while they are on a limb. Try it, you'll see. Enjoy.