[ShrimpBurrito]

I'm not sure water putty is doing to do the trick as there isn't much for it to hold on to. If you just wanted to fill a void, that's one thing, but you are expecting the putty to hold a screw.

You could glue a new piece of plywood to the underside of the countertop, and screw into that. It doesn't have to be as large as the existing countertop -- just some 2" or so wide strips that run along the edge where the screws go. (So called plastic lumber may even hold the screws better, but I haven't worked with it so I don't know.)

Not knowing where exactly that countertop rests, doing that will probably raise the countertop by the thickness of the new plywood. If that's a problem, you could cut off a bit of the cabinet where that counter rests on.

Assuming the screws are there to hold the countertop and not the range, you might also just consider gluing that countertop down as is with some strong woodglue, like Titebond III. That way you won't need screws. Construction adhesive would also probably work fine. Someone here recommended the PL brand of polyurethane construction adhesive as working very well....it's at Home Depot.

Dave