Why does this 757 have a propeller engine attached to the fuselage?
From the description below the image you linked:


  The Honeywell, Boeing 757 test bed appeared on static display for a few days before departing half way through the event.


A testbed aircraft is an aircraft used for flight research or testing new equipment such as engines.

You can see other photos without engine or with a jet engine instead of a propeller one.

The engine is not needed to fly, but is being tested, and apparently that position has been deemed a good solution to the problem "where do we attach an extra engine we need to do tests on?".