If you want a keyboard that synchronizes your clipboard and tasks across your phone and computer, Microsoft SwiftKey is worth a look. It's got cloud clipboard, task capture and multi-language typing abilities across Android and iPhone devices. This customizable keyboard learns your writing style to speed up your typing and improve accuracy, making it a good option for productivity.
Another contender is Slate. It's not a task-syncing keyboard per se, but it's an AI-powered mobile keyboard designed to help you be more productive on your phone. It's designed to let you write, take notes and create art on your phone the way you would on a laptop, so it's a good option if you need to be productive without a laptop or desktop.
If you want a more complete productivity package, check out Taskade. It's not a keyboard, but it's a workspace for tasks, research and collaboration that includes AI-powered tools to generate workflows, collaborate in real time and share projects across devices. That can help you get your productivity in order, and it works with lots of devices so you can keep your tasks and clipboard in sync.