The solution is original from https://superuser.com/a/1519694 , I copied it here for convenience.

Using SSH keys for multiple accounts

If you need to connect to the same host with different keys then you can achieve it by:

Configure the ~/.ssh/config with different Hosts but same HostNames. Clone your repo using the appropriate host.

Example:

Host work
 HostName bitbucket.org
 IdentityFile ~/.ssh/id_rsa_work
 User git

Host personal
 HostName bitbucket.org
 IdentityFile ~/.ssh/id_rsa_personal
 User git

Then instead of cloning repos like:

git clone [email protected]:username/my-work-project.git
git clone [email protected]:username/my-personal-project.git

The host name should be used for cloning:

git clone git@work:username/my-work-project.git
git clone git@personal:username/my-personal-project.git

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