At a minimum, the print head drive and the head park mechanisms are out of synchronization.
First, is this still under warranty?
Or less than 2 years old?
If so, I suggest that you take it to an authorized Epson service center.
There are just too many things that you can damage if you don't know what you are doing.
Otherwise; How mechanically inclined are you?
The only way to fix this kind of problem is to tear down the printer and operate the mechanisms manually.
I would tear the whole print mechanism apart and clean the paper and ink paths while I had it apart.
Check the belt and pulleys for wear and damage.
If either is damaged, you will need to contact the Epson service center to get replacement parts.
Aligning the head and mechanism can be tricky.
Look at the belt and pulleys carefully.
There should be some marks for alignment.
But, like I said at the top, you are likely better off taking this in for service.
Unless, the unit is worth less than the service charge.
Chas