I had faced the similar problem with the GitHub. I can assure you that it is very easy to solve it.
1. Generate the SSH key on the computer as described in following link : Generating SSH keys.
2. Now Login to your GitHub account using following link : GitHub Login.
3. In your account, you need to add your newly generated SSH Key using following link: My account SSH keys.
4. Finally you need to try again to git clone the project.
I also faced the similar issue in the recent past. I did the below procedure and it started working for me:
1. Generate the Keys from your GIT GUI client on the Windows. And Copy this key to your clipboard.
2. Now open up the account on the bitBucket/ git website, and try to add the key to your profile. This way, your server will know that you are the legitimate user who is trying to access from the legitimate system.
3. That is it. All push commands worked for me after following above procedure.