I owe my interest in Blue Jays to a woman from Minnesota (I think) who followed and actually befriended an extended band of Blue Jays for years. She spent years doing it, and could recognize them as individuals, something I have been unable to do.
If you enjoy birds, her extensive YouTube Channel has a huge amount of entertaining and informative content. She is called "Leslie The Bird Nerd", and has extensive footage of her observing and interacting with the Blue Jays and other birds: LINK: Leslie The Bird Nerd YouTube Channel
People on this thread are correct, Blue Jays do have a bad reputation for being bullies, and well deserved as I have personally observed a Blue Jay actually brutally murder a Sparrow that it took issue with (more about that later in this post) and they also raid nests, that kind of thing. But nature is nature. And it most certainly can be (and often is) cruel.
In the last 15 or 20 years, I have grown increasingly interested in birds, where I don't consider myself just a bird watcher, I observe their behavior and have delved deeper into it, as well as their physical characteristics and life patterns. (LOL, part of it is that I parted ways with the NFL a few years back after being a nearly rabid fan for more than 50 years, and I can't play sports anymore, so...I observe birds!)
Birds are one of the few animal species that doesn't run away when they see us humans. They stay close, where we can watch them, but they are also avid watchers of humans. When I lay out in my hammock, there is a lot of bird activity around me, and with my binoculars, I can see birds that are far away, and it is clear that they are directly and intently observing me from hundreds of yards away.
I have about 60 life goals I wrote down before I retired, and one of them to get a Blue Jay to eat out of my hand. That will probably never happen, though, but...I have seen someone do it so it is possible. (I have gotten a variety of wild birds like Chickadees, Juncos, and Titmouses to eat out of my hand, so it gives me a goal.
Here is a Tufted Titmouse eating from my hand:
Blue Jays and Crows are members of the Corvid family, and I am fascinated by both groups, but I love Blue Jays because while Crows are very intelligent birds, they are far more reserved and I dare say, predictable than Blue Jays.
Did you know that Blue Jay plumage isn't really blue, it is gray? If you pick up a Blue Jay feather off the ground, they aren't blue. They only appear blue on the bird because of the way light refracts in the feather. (Unlike Cardinals, which are actually red, and it is the food they eat that causes the red color)
Blue Jays are classified as songbirds (as are Crows) but you wouldn't know it from hearing their noisy jeering call. However, their vocabulary is very deep, and once you understand it (as much as we can understand it) it is fascinating to watch them, and you understand their lifestyle and social groupings.
They are very clannish birds, and they have an interesting repertoire of calls.
They have the Jeer call, which we all know, and it has a variety of uses. The most obvious use is a warning when there is a perceived threat such as a hawk, a cat, or even occasionally, another Blue Jay from a different flock. But the Jeer Call is also used to communicate with other Blue Jays, usually their mate. (They mate long term or for life) They use the "soft" Jeer Call to communicate their location, and they ping each other with it. If you listen to it carefully, the "soft" Jeer Call is different from the "hard" jeer call which is used for serious threats, and has a distinct, and to some, annoying edge. When they use the "soft" jeer call, they are "pinging" their mate or friend, who will then answer back, often from far away, with a "soft" jeer call in response. The hard "Jeer" call, which has nearly an edge of hysteria to it that is missing from the "soft" jeer call.
They have the amusing pump handle group of calls such as the "Squeaky Gate" call. When they do it, they bob up and down when they do it, and I do find it funny to watch, especially when you see a bunch of them doing it all at once, bobbing up and down! It is however, a low-to-medium threat alert when strange Blue Jays are around or a female is being approached by a male that is not her mate. It is also a mating call.
They imitate hawk calls to scare other birds away from a bird feeder.
They have a quiet language called the "Interpair" call, and a related one called the "Whisper" call.
And they have a group of calls called the "Rattle" call. Only females do this call, and it is the only way I have ever been able to tell the difference between a male and a female Blue Jay.
For years, at work, I kept a bird feeder outside the window of my office (which bordered a large copse of trees and heavy vegetation) which I often kept open, and throughout the day, would line up peanuts in the shell along my window sill. The Blue Jays and Titmouse would fly up, land on the open window just a foot or two away, and choose their peanut before flying away with their booty to cache it somewhere!
I had that bird feeder out there for about 15 years, and while I never could tell individual Blue Jays apart, I definitely knew it was the same band. (a group of them is called officially a "Scold", which I love). They were not as afraid of me as any random group of Blue Jays might be. I usually got to work around 6:15-6:30AM each day, and when I opened the blinds to my office, I would see as many as 20 Blue Jays just sitting in the trees, waiting for me to put out the peanuts. (When I walked out the short, enclosed walkway, they would see me, and I could hear the morning stillness broken by that soft "Jeer" they use for communication as they seemed to say "The bald guy with the lab coat who puts out the peanuts is here!"
My morning ritual was to get everything set, put on my lab coat, turn on my computer, look for any immediate issues that needed addressing, then I would put my coffee on, grab a gallon sized bag of bird seed that I brought in with me every day, and I would go out in all weather and fill the bird feeder (one of those ones that if a squirrel jumped on it, it would spin around and throw them off). Then I would go back inside, get my coffee, check the computer again, and open the window.
Here is a video I took of my squirrel-proof bird feeder and marked up for the 2020 election, but you can see the squirrel refusing to let go!
I would begin by throwing peanuts one at a time out onto the ground about 20 feet away. That was how I counted them, because they had a very distinct pecking order. They wouldn't fight-they knew who was the next to fly out for the next thrown peanut. I would throw a peanut and count it, then when it was grabbed, I would throw another. I would repeat this until I threw a peanut that would sit there with no Blue Jay to pick it up. So on any given day I could count 5-20 Blue Jays present.
As each Blue Jay got a peanut, it would fly, as if the devil were chasing it, as fast and directly (as if with great impetus and purpose) as it could to a perch somewhere. There, it would pin the peanut to a brand, and begin pecking it as if it were a woodpecker to break it open.
And there were the ever present squirrels, who the Blue Jays did not mess around with.
Incidentally, when a bunch of Turkeys are around, NOBODY messes with the Turkeys. All the birds and the squirrels give them a wide berth. And they would ferociously go after any peanuts I threw out there, even pecking the head of some lesser turkey that had the temerity to pick up a peanut out of the "pecking order"...you can see them looking up at me expectantly here:
So, if there was a squirrel sulking about, pretending not to notice I was about to throw a peanut, there was almost always a Blue Jay sitting nearby in a shrub or tree, watching for it as well. What I would do is throw the peanut as far as I could away from the squirrel, which a split second before had been nonchalantly poking around as if it didn't know what was going on, but as soon as I threw it would run hell-bent for leather directly for the thrown peanut. But If I threw it correctly, the Blue Jay could immediately swoop over at the same time and scoop up the peanut a split second before the frustrated squirrel could reach it.
Then, as the squirrel sat there with its sides heaving, I would throw a peanut in the exact opposite direction as far as I could, and the squirrel would resolutely gather itself up and run full speed towards it, but another Blue Jay would swoop down and snatch it before the squirrel could arrive. Interestingly, the squirrel usually got the nature of this exercise pretty quickly, and if I threw another peanut in the other direction, it would decline to contest it.
Another thing about Blue Jays-they definitely understood the concept of greed. (I know I am anthropomorphizing them, but it is undeniable to me they get "greed") If I threw out two peanuts at the same time, it was hilarious to watch the occasional Blue Jay try to pick up both of them. They would try and try unsuccessfully to get the peanut into its throat pouch (because a whole peanut is just a little too big to get down, and it looked like they were determinedly choking or gagging, but would not give up. Most of the time they would then fly away. But once, I watched one try and try and try, then with dogged determination, while holding one peanut in its mouth, it impaled the other one on its beak before flying away!
But one of the most amusing behaviors to me is their desire to get the biggest peanut. Even if the size differential was slight, they invariably and without fail would discriminate and take the slightly bigger peanut. If I threw out two peanuts of totally disparate sizes, the Blue Jays with 100% reliability would snatch up the biggest peanut first and fly away as if the Devil itself were chasing it.
But if I carefully chose two peanuts of almost exactly the same size and shape and threw them out at the same time, the Blue Jay would fly down, and pick one up. Then, eyeballing the other one, it would drop it and pick up the other one. Then, as if totally mired in indecision, it would release that one and pick up the first one again. I counted one Blue Jay do this five times before it seemed to decide in irritation there was no difference, and it flew off with one of them!
I saw one pick up a peanut one day, and as it flew away, I threw out another peanut that was far larger, and the Blue Jay did a sharp 180 turn, landed, spit out the smaller peanut and picked up the bigger one before flying away with its prize! It was hilarious! It spat out the peanut it had with such disdain that I swear I nearly heard it go "Pah!" as it ejected the smaller peanut in disgust!
Finally, the "Sparrow Murder". I know this completely sounds like imparting a characterization of a human behavior on a wild animal, but it was exactly that.
It wasn't for food, and there was something quite deliberate and sadistic about it.
I had my window open one morning working, and I kept hearing this really annoying animal sound, but I continued working, but after a while of trying to ignore it (even closing the window) I stopped working to investigate what was making it.
As I looked out the window, I could see a Blue Jay on the ground, pecking at something I figured was some small animal of some kind, like a mouse. I couldn't stand that that horrible sound, so I decided I had to end it because I couldn't work.
I walked outside, and as I walked around the corner towards the feeder, I could see the blue jay standing on the sparrow, deliberately pecking. It looked up and saw me, and as I walked closer, it took one more peck, then flew away. 
The sparrow had its eyes pecked out, and oddly, there was sparrow blood all over its head. I guess those little birds didn't even seem like they had blood in them. But it was quivering and making noises, so I just put it out of its misery with the heel of my shoe.
Seriously, there was a specific sense of malice on the part of that Blue Jay. It wasn't killing it to eat it because it could have easily done that in seconds. It was almost as if it had a vendetta against that sparrow for something, and was making sport of killing it because it LIKED killing it with malice. Never thought I would anthropomorphize an animal like that, but I couldn't explain it any other way.
When the Blue Jay saw me appear around the corner of the trail to walk towards it, it took one, last...defiant peck. There was a feeling of "How do you like those apples, you effing sparrow piece of crap?"
So yes...they can be pretty mean animals. But that is part of nature, just as it is in us, I think. But in spite of that, I love watching them! They can be bullies and cruel..."Dicks" as it were, but their behavior is interesting and often amusing to the point of buffoonish clownery!