You develop on master. if you need s 'stabilisation' phase, when you only do bugfixes you can do that on a release branch. Or if you usually deploy the latest you can just tag the version that you deploy. If you want to just fix something from the currently deployed version you can create a 'hotfix' branch out of the tagged release version, do the fix, deploy, merge the hotfix branch into master and delete it:
git branch hotfix v1.2.3
git co hotfix
# do the fix
git tag v1.2.4
# deploy
git co master
git merge hotfix
git branch -d hotfix