Veneered boards can probably be cut to size on a bandsaw, (Veneer upermost ), with a fine tooth blade (The finer the better to avoid chipping. ) The infeed needs to be fine also.
Personally would cut slightly over size and then sand back to size, for just that reason.
MAKING veneers on a bandsaw would be impossible, I suspect, A veneer is very thin timber, probably 0.127 mm ( 127 microns ) thick or so; extremely fragile.
You wpu;ld need to set a fence which limited the depth of cut to aminute amount.
The usual means of making a veneer is to shave it off from a rotating workpiece, where the work rotates against a stationary blade; rather llike a mirror image of a wood planing machine operation, where the blade rotates against the work, to produce thin chips.
Study some woodworking books to find the methods used.
Howard.