I have changed the openssh-server startup script to not run "ssh-keygen -A" upon extension loading, and this is also how the startup of openssh.tcz in the regular Tinycore repo behaves upon looking at its startup script.
Before starting the SSH server, run as root "ssh-keygen -A" and then back up the /etc/ssh directory to save the generated key files. Or use the specific commands to generate the desired keys:
ssh-keygen -A (will create dsa, ecdsa, rsa, and ed25519 keys)
ssh-keygen -t dsa
ssh-keygen -t ecdsa
ssh-keygen -t ed25519
ssh-keygen -t rsa
ssh-keygen -t rsa1
Other files to back up such as to keep the same user and password are mentioned in other posts in this thread.
The ssh server is started with the below command -
/etc/init.d/ssh start