Best method of pushing content changes that contains paragraph fields from dev to production?
One recommendation is to use "Features" to generate:


a Feature export of any config changes to the content types, paragraph bundles, and fields
a separate Feature export of the content/nodes themselves


To accomplish this, you'll need:


"Features" module:  https://www.drupal.org/project/features
"Features Extra" module:  https://www.drupal.org/project/features_extra 
"UUID  Features" module:  https://www.drupal.org/project/uuid_features
"Strongarm" module:  https://www.drupal.org/project/strongarm
"Diff" module: https://www.drupal.org/project/diff


NOTE:  this approach generally works well, as long as the effected content/node IDs between production and your staging/dev environment are the same.