These are the fidgets that I use the most. They're pocket sized bead loom woven squares. These come in a few flavors, but at the core, they're basically the same: A neat little pocket fidget you can fiddle with like a toy with a nice texture and flexibility, that's quiet enough that you won't be bothering anyone else nearby when you pull it out.
The round-bead ones come in two types: Ones made with large beads, and one made with small beads.
The large bead ones are made with 4mm rondelles (the type of bead that's basically doughnut shaped.) Because of the size of the beads, the beads roll easily, making them best for anyone who's likely to rub them against their skin, or rub them super fast. When broken in, these have a wonderful drape that lends itself to roll-flipping and other motion.
The smaller round beaded squares are stiffer, but have a really detailed texture, best for someone who likes a more sensory than fidget sort of stim. The beads still roll, but make take a bit more effort. These also can have more detailed patterns and are best for showing off (for example, if you want to clip it to your badge holder or similar where it'll be seen more)
For a different sort of square, also check out the Cube Bead variations!
In general, these squares have a small clip off one corner that allows them to be hooked on to backpacks, notebooks and various other places, and they're all small enough to be carried in a pocket. Larger round bead squares tend to be about an inch and 2/3rds, with the smaller beaded versions being more towards an inch square, and the cubes being up to about 2 inches.
All variations are made with a strong beeswax infused thread and can stand up to repeated fiddling, rubbing, hand washing and even some gentle chewing. (Just avoid letting them take a ride in the washing machine if at all possible! That was how I killed my favorite one after about 6 months of abusing it.) Fidgets may start out a little stiff, but will loosen up and become more pliable as they're played with.
If you have a specific color or pattern you'd like made into one of these fidget squares, send an email to firstname.lastname@example.org and I'll let you know if I have the beads to make it!