My question is partially duplicate of Moving uncommitted changes to a new branch
However, The trick is, I made changes to few files which belong to a sub-module.
My Primary repo: /testing
Sub-module is at: /testing/lib/xyz
git checkout -b new_branch
A sub module is a git repo: you can create a branch there to reference your new changes, just as explained in "Moving uncommitted changes to a new branch".
Then reset its content to its own
I would advise to push that branch to the submodule remote origin repo, in order to avoid keeping those changes purely local.