There are few more frustrating places to find your ball than against the greenside fringe.
When you are struggling to make solid contact with the ball, there are a number of methods that can be used to navigate the annoying fringe grass surrounding the green.
First option would be to use a rescue club, with its wide sole cutting through the snagging grass best of all. Gripping down and adopting your standard putting set-up as much as is feasible allows the ball to roll toward the hole as smoothly as possible.
Alternatively, hover the putter above the cut of grass, with the aim of intentionally hitting halfway up the ball, so the fringe offers no interference. The only danger is that the ball can hop during the initial part of its journey offering inconsistent distance control, and be aware that it will tend to release a little more due to an increase in overspin.
The final option uses the belly wedge, aiming to strike the ball at roughly its equator while using the bounce on the sole to cut through the very top part of the fringe, in order to get as little resistance as possible. An accurate contact is required, but you get a true roll.