Should Navigation menu have a fix position in application with greater width?

It depends on the usefulness of the menu. If it’s extremely likely to be used frequently, yes, definitely good UX. However, you have to consider the size of the menu versus the total screen real-estate. If you are targeting a mobile device or small screens and your menu bar is too big, the loss of screen real estate may out-weigh the convenience of the menu’s persistence.

Rule of thumb is that the top 18% of controls should be maximally accessible, but again, are you willing to sacrifice the space?