Best solution can be:
Add a string parameter in the existing job 
Then in the Source Code Management section update Branches to build to use the string parameter you defined 
If you see a checkbox labeled Lightweight checkout, make sure it is unchecked.
The configuration indicated in the images will tell the jenkins job to use master as the default branch, and for manual builds it will ask you to enter branch details (FYI: by default it’s set to master)