It seems like there are no pre-built wheels for python 3.10 in the Autopy project page at PyPI.The latest support python 3.8.
So you will need to compile for your operating system.
From the documentation.First, see if a binary wheel is available for your machine by running:
$ pip install -U autopy
If that fails you'll need to install the rust compiler using rustc and then run:
$ rustup default nightly-2019-10-05
$ pip install -U setuptools-rust
$ pip install -U autopy
Another option is to build from the latest source on the GitHub repository:
$ git clone git://github.com/autopilot-rs/autopy-rs.git
$ cd autopy
$ make
$ make install