Hi @Plotva,
Welcome to the Atlassian Community.
To create a new branch in Bitbucket Cloud just click on Branches and you will see a Create branch button. In Bitbucket Server, click Create branch on the left side menu bar.
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Okay, so in this case your repository is empty, so the only way to create a branch in it is to first clone it and then do a commit in the repository. The initial commit will create the master branch. Once that is done you need to push your commit back to Bitbucket and then you will be able to create branches from within Bitbucket.
I would recommend that you checkout the Bitbucket tutorials and also Atlassian's Getting Git right.
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