Hi Cleminson,
I see that the printer "prints a few pages, moves into a cleaning mode and then indicates there is either a misprint or paper jam in the paper tray".
I will be happy to help you.
Make sure the printer is connected directly to a wall outlet. (don't use a power hub or a surge protector)
What drivers are you using for the printer? (Apple drivers, downloaded drivers)
Here is a link to the Full Software Solution drivers if you don't already have them installed.
HP LaserJet Pro CM1415fn color MFP Series Full Software Solution - OS X 10.9 Mavericks.
Check the driver name that is installed for the printer. The Airprint driver might be installed instead of the Printer's driver. (usually defaults to Airprint)
Click the Apple menu and then click System Preferences. Click Printers & Scanners, highlight the printer name on the left side and on the right side of the screen should show the name.
If the printer name shows Airprint then that is the Apple drivers, delete it and add the printer name back in from the list. Click the - sign to delete the driver and then click the + sign to add the driver, might have to click the drop down to select the printer's name to add it in.
Here is a document to run a cleaning page through the printer's control panel.
The Attention Light Blinks and a 'Paper Jam' Message Displays on the Control Panel.
You can check for paper jams.
Then go to Step five: Print a cleaning page.
What is the weight and type of paper you using?
Try another application to see if you have the same issue.
Let me know the results.
Thank you for posting on the HP Forums.
Have a great day.