The Fixing Charm (incantation unknown) is a spell which fastens an object in place. Its effect is similar to that of the Permanent Sticking Charm, but is most likely reversible. It may simply be another name for the Sticking Charm.
Elveira Elkins wrote to the advice page of the Daily Prophet because she was having difficulty getting this charm to work and was told by Zamira Gulch that her mind was probably wandering whilst 'charming' and to just use nails.
Behind the scenes
The Epoximise spell may be a variation of the Fixing Charm, or even the incantation for the actual charm. This appears to not be the case since Epoximise, which is from the Harry Potter Trading Card Game, is labelled as a Transfiguration spell on its card, not a Charm. However, errors have been found with other cards. For example, Diffindo is incorrectly labelled as a Transfiguration spell in the card game.