How to properly install a Composer project?

Question

Composer

The essence of the question is as follows, I will immediately make a reservation that there is a ssh key. I'm trying to get a project from composer (project on bitbuket) but I get this error
Cloning into '/var/www/clientportal.lc/vendor/...'...
Permission denied (publickey).
fatal: Could not read from remote repository
because it’s not clear to me what the permissions are and it takes a long time to wait for these decisions, I received the project via git clone, now the question arose of how I could connect the specified repository to my project (Laravel) without downloading it.