Fixing chipped table corner
That's more than just "varnish". It is some sort of thin material, most likely plastic laminate or similar. You can't just "patch it" beyond the tiniest of holes or cracks - and that damage is far beyond that.

I suggest getting something either really similar color or nicely contrasting to use as a corner bumper/guard. If you put it on all 4 corners then it may actually look like it was designed that way. Unfortunately, most of what I have found so far is designed for childproofing - i.e., cushioned. Unless you actually need childproofing as well, I would recommend something thinner as it will look more "natural".