how to git push to a local branch?

Use git merge instead to manipulate local branches.

git checkout master
git merge B
git merge C

If you really want to push a local branch to another local branch, git push . B:master, though this is quite rare.

While on the master branch, have you tried

git merge B

This should merge your local branch B back into master, same can be done for branch C

https://git-scm.com/docs/git-merge

As others said, normally you want to switch to A and then merge from B instead.

However, if you do it regularly, in some edge cases it makes sense to set A as upstream branch for B

git checkout B
git branch --set-upstream-to A
# shorthand: git branch -u A

and then use git push from branch B like you asked.