how to pass project parameter as branch name to build in Jenkins

This issue has been reported several times. This works if you disable the "Lightweight Checkout". Apparently the code path is very different if you are using the lightweight checkout, and that has not been resolved, apparently.

See JENKINS-28447

You can use git parameter plugin ...

then in paramerterized select Git Paramerter ..Give any Name e.g. BRANCH select parameter type as "Branch" and put default value for branch. Then in Branches to build inthat put ${BRANCH}. Build job with parameter as branch name...