A screenshot will help tremendously in this case.
Otherwise I would just say settle on the river for +25% trade bonus route gold if you're playing BNW.
If I understand OP, he's basically asking if the capital can't be both on a hill and along a river at the same time but can be either on a hill or on a river which would we choose? (And unlike the earlier "trilemia" thread there's no mountain anywhere near here)
For me that's river: Water mill amounts to a second granary in addition to base hammer.
If not interested in all that food, just relocate a worker to a mined hill.
Without further info Id build on the river - but sometimes with your starting settler you'll later discover the city will be built on a strategic resource. Not that that's a particularly bad thing - you get the resource instantly of course - but you don't get the benefit of improving the tile.
This really needs a screenshot to answer properly. The answer depends mainly on the shape of the river, and possibly resource placement. There needs to be a good reason to move off a hill...that +1 production really snowballs. If you can reach enough riverside tiles to have good food without moving your settler than I would settle in place. But if the river is shaped in a way that prevents you from accessing enough riverside tiles, then I would probably move. I certainly wouldn't move next to the river JUST to build a watermill while losing 1 hammer per turn.
if moving to river loses you a luxury, dont. if moving to the river gains you a luxury, move. if neither, found on river because rivers have greater benefits than hills. However, a scrrenshot would help.
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