I'm not sure about specifics but when I was looking for android devices with small screens (like 3") last time, I found some indian smartphones. They were ultra-budget and I wanted something premium so I didn't pursue it further, but it was definitely something I never saw in the public market.

Another specific niche might be babushkaphones. It's a cell phone made for babushkas. Basically huge buttons, screen with huge fonts, dumbed down interface so people with very little technical knowledge could use them to be on line.