My old belt had the cogs on the inside. My new belt the cogs are on the outside, came that way in the packaging. What is the correct way for the belt to go on? I know this is a crazy question because I have replaced several belts on different cars/trucks for years. Thanks in advance....

Are you sure you have the correct belt?  Does the belt just need to be turned "over"?  What "cogs" are you referring to?  What vehicle are we discussing?

92 Sammy. One side of the belt is smooth and the other side has cogs. I'll try to attach a photo.

A 92 Samurai takes a vee belt, some vee belts have teeth or as you say "cogs" on the inner surface, some don't, I've never seen one with teeth/cogs on the outer surface.  Look at the edges of both the old & new belts - there should be a noticeable taper or vee (hence the name) - the vee has to match the pulleys on the engine, so the narrow part of the vee sits lower down in the pulleys.