I have a problem when I push my codes to git while I have developer access in my project, but everything is okay when I have master access. Where is the problem come from? And how to fix it?
Error message:
error: You are not allowed to push code to protected branches on this project.
...
error: failed to push some refs to ...
there's no problem - everything works as expected.
In GitLab some branches can be protected. By default only 'master' user can commit to protected branches. master
branch is protected by default - it forces developers to issue merge requests to be validated by project master before integrating them into main code.
You can turn on and off protection on selected branches in Project Settings (where exactly depends on GitLab version - see instructions below).
On the same settings page you can also allow developers to push into the protected branches. With this setting on, protection will be limited to rejecting operations requiring git push --force
(rebase etc.)
Since GitLab 9.3
Go to project: "Settings" -> "Repository" -> "Expand" on "Protected branches" 
I'm not really sure when this change was introduced, screenshots are from 10.3 version.
Now you can select who is allowed to merge or push into selected branches (for example: you can turn off pushes to master
at all, forcing all changes to branch to be made via Merge Requests). Or you can click "Unprotect" to completely remove protection from branch.
Since GitLab 9.0
Similarly to GitLab 9.3, but no need to click "Expand" - everything is already expanded: Go to project: "Settings" -> "Repository" -> scroll down to "Protected branches".

Pre GitLab 9.0
Project: "Settings" -> "Protected branches" (if you are at least 'Master' of given project).

Then click on "Unprotect" or "Developers can push":

for the GitLab Enterprise Edition 9.3.0
By default, master branch is protected so unprotect :)
1-Select you "project"
2-Select "Repository"
3-Select "branches"
4-Select "Project Settings"
5-In "Protected Branches" click to "expand"
6-and after click in "unprotect" button
I experienced the same problem on my repository at https://framagit.org. I'm the master of the repository, but I had such an error.
I've unprotected my project and then re-protected again, and the error is gone.
Framagit has upgraded the gitlab version between my previous push and the problematic one. I suppose that this upgrade has created the bug.
Hope that this can help someone else not losing their time.