I have a submodule with another token, how can i set build-push-action?

#1 [internal] load git source https://github.com/TarsCloudMarket/CountServer.git#4c66a29c33814cc24e93ed470d4a1ccc3ed98b05
#0 0.041 hint: Using 'master' as the name for the initial branch. This default branch name
#0 0.041 hint: is subject to change. To configure the initial branch name to use in all
#0 0.041 hint: of your new repositories, which will suppress this warning, call:
#0 0.041 hint: 
#0 0.041 hint: 	git config --global init.defaultBranch <name>
#0 0.041 hint: 
#0 0.041 hint: Names commonly chosen instead of 'master' are 'main', 'trunk' and
#0 0.041 hint: 'development'. The just-created branch can be renamed via this command:
#0 0.041 hint: 
#0 0.041 hint: 	git branch -m <name>
#0 0.042 Initialized empty Git repository in /var/lib/buildkit/runc-overlayfs/snapshots/snapshots/1/fs/
#0 0.097 fatal: Not a valid object name 4c66a29c33814cc24e93ed470d4a1ccc3ed98b05^{commit}
#1 0.598 From https://github.com/TarsCloudMarket/CountServer
#1 0.598  * [new branch]      master     -> origin/master
#1 0.606  * [new tag]         v1.0.0     -> v1.0.0
#1 0.716 Submodule 'libraft' (git@github.com:TarsCloudMarket/libraft.git) registered for path 'libraft'
#1 0.719 Cloning into '/var/lib/buildkit/runc-overlayfs/snapshots/snapshots/2/fs/libraft'...
#1 0.974 Warning: Permanently added 'github.com' (ED25519) to the list of known hosts.
#1 1.086 git@github.com: Permission denied (publickey).
#1 1.088 fatal: Could not read from remote repository.
#1 1.088 
#1 1.088 Please make sure you have the correct access rights
#1 1.088 and the repository exists.
#1 1.089 fatal: clone of 'git@github.com:TarsCloudMarket/libraft.git' into submodule path '/var/lib/buildkit/runc-overlayfs/snapshots/snapshots/2/fs/libraft' failed
#1 1.089 Failed to clone 'libraft'. Retry scheduled
#1 1.093 Cloning into '/var/lib/buildkit/runc-overlayfs/snapshots/snapshots/2/fs/libraft'...

Start with the build-push-action configuration and the reported Git submodule clone failure, focusing on how credentials are supplied for the nested repository. Confirm the documented setup can authenticate the submodule and complete the image build without the publickey error.