Like almost all the other weapon props used in the Original trilogy, the design of the 44 was based on an actual weapon. In this case, the German "Broomhandle" Mauser pistol was used and modified. The Mauser is the same weapon upon which the DL-44 heavy blaster pistol (popularized by Han Solo) was built.
To make the Model 44, various odds and ends were attached to the Mauser, as well as certain pieces (most notably, the Mauser's long barrel) being hacked off.
The Power 5 heavy blaster pistol was also based on the German Mauser. The most noticeable difference between it and the 44 is the Power 5's flash suppressor and full barrel.