Will a Dodge pickup drivers side door from 2008 four fit 2001 quad-cab?

No, a 2008 Dodge Ram pickup driver's side door will almost certainly not fit a 2001 Dodge Ram quad cab. While they might be the same brand and body style (pickup), the body styles changed significantly between those model years. The door's mounting points, window mechanisms, and overall dimensions are likely different enough to prevent a direct swap.