First question: how "antique" is this mug?
I don't have the expertise to make an educated guess, but at least to me this doesn't look like a cheap mug made to look old.
Usually the older an object gets, the more valuable it gets. But an incompetent repair attempt will completely diminish the value of the object because fixing the botched repair attempt can be even more expensive than a professional repair would have been in the first place. So if this mug is actually a valuable antique, do not attempt any restorations on your own. Trust an experienced restorator with this task or keep the mug as it is and let it reflect its long history.
If you insist on repairing it, be aware that it's a multi-step process that involves gluing, sculpting, sanding and painting. This in not done in an afternoon.
There are different ceramic fillers and 2-part epoxy clays available for exactly this scenario, like Milliput. Since the chip is quite big, I would recommend using a special glue in addition to ceramic filler to ensure a strong bond, as demonstrated in this video by The Ceramic Repair Studio.
The steps include:
- Clean the chip with alcohol to remove any oil or dirt. Wash your hands very thoroughly before handling the object or wear gloves to avoid introducing fresh skin oil into the chipped area.
- (optional) Mix ceramics glue like Araldite in the recommended ratio. Apply a thin layer over the chipped area, but not over the remaining glaze.
- Mix 2-part epoxy clay or ceramics filler in the recommended ratio and press it firmly on the chipped area. Form the clay in the desired shape but make sure to overfill the chip.
- Let the filler cure completely.
- Sand the cured filler down to the shape of the original object with fine sand paper (approx. 200 grid).
- Paint over the filler with acrylics paints to match the original color.
- Apply one or several thin layer(s) of clear shiny varnish to blend the repair into the glazing.
The entire process in described in detail in this article by Lakeside Pottery. By searching for "repair chipped ceramics" you'll find a lot more instructions, some more professional than others. My advice is to listen to ceramics creators and restorators rather than DIY channels.