you can use an indoor adhesive to fill the chipped area, paint it, and glaze it to fix it. there’s different adhesives and glazes out there so I would recommend looking into what the mug’s made of and trying to match materials. Keep in mind that if it’s dishwasher/microwave safe the adhesive/glaze you use might affect that

You can also use a polymer clay and glaze to fix it. Keep in mind polymer clay needs to bake to set so the mug HAS to be dishwasher safe (since it’ll be able to withstand high heats!)