In Jenkins' global config set "docs" as default branch in section "Global Pipeline Libraries" for Libraries "deliveryLib"

enabled "Allow default version to be overridden"

Use "Legacy SCM" along with "Git" and add into "Branches to build" section with mutlit-branches: e.g */master */docs */fixes

In Jenkinsfile, tried out different combinations.e.g:

@Library('deliveryLib@master')

or

@Library('deliveryLib@origin/master')

or 

@Library('deliveryLib@fixes')

but all failed, as log shows:
Checking out Revision *************** (origin/docs)
 

Not 100% sure, if this error was caused by

system cached last time "default branch name"

or

the overwritten functions not work

or

checkout was sorted by some alphabet order

Current solution is, to remove other branches name, but only leave the one really want to use in system config, followed a jenkins restart