An example of how I use Git submodules.
And that looks a little bit like this:
git init
vi README
git add README
git commit
git submodule add git://github.com/XXXXX/xxx.yyyy.git stm32_std_lib
git status
git submodule init
git submodule update
cd stm32_std_lib/
git reset --hard V3.1.2
cd ..
git commit -a
git submodule status
Maybe it helps (even though I use a tag and not a branch)?