I recently replaced the linoleum counter top in my kitchen, as well as
the sink. My problem is that there is a quarter inch gap between the
top-mounted sink and the backsplash and I need suggestion on what to
do with this gap.

The countertop is 26 inches in width from the wall to the front edge.
The rolled backsplash is 1.5 inches thick, which leaves about 24.5" of
counter space. The sink is 22" front-to back. the countertop
overhangs the front of the cabinet by about 1.5".

So the back of the sink is about .25" from the backsplash.
Unfortunately, I'm not sure of the best way to finish this. Should I
caulk it with cleal caulking (which I think will be hard to clean),
just leave the gap, or is there any other solution?