The Date Time custom field does not comply to the rules of configuration of "Date/Time Formats" from the Look and Feel. Kindly refer to the attached screenshots.

Example: Complete Date/Time Format dd/MMM/yy HH:mm

Workaround prior to 4.4

1. Shutdown JIRA instance
2. Create the jira-config.properties in your JIRA Home Directory
3. Insert the following into the file (example: dd/MMM/yy HH:mm) or other format that you want to have

   jira.date.picker.javascript.format = %e/%b/%y
   jira.date.time.picker.javascript.format = %e/%b/%y %H:%M
   jira.date.time.picker.java.format = dd/MMM/yy HH:mm
   jira.date.picker.java.format = dd/MMM/yy
   

4. Delete the contents of JIRA Installation Directory\work directory
5. Restart JIRA instance

Workaround 4.4 and later

1. Go to General Configuration > Advanced
2. Configure the format as below

   jira.date.picker.javascript.format=%e/%b/%y
   jira.date.time.picker.javascript.format=%e/%b/%y %H:%M
   jira.date.time.picker.java.format=dd/MMM/yy HH:mm
   jira.date.picker.java.format=dd/MMM/yy