In 者 as a component, the form with an additional dot (者) is the one considered 'orthodox' in the sense it appears in the Kāngxī Dictionary. This does not mean that it is somehow more etymologically correct compared to the dot-less form; as most of these 'orthodox' forms, this one was created by the authority of the Shuōwén jiězì, which assumed the character to contain 白 (to my knowledge, actually the character 者 developed from a pictogram of a sugarcane, originally writing the word *tAk-s 'sugarcane' and borrowed for the similarly pronounced grammatical particle *tAʔ > zhě, so there is no 白 in the character).
However, in most of the regions, the dot-less form was more prevalent despite the injunctions of the normative dictionaries, and in modern times it was the one that was standardized. In fact, 者 without a dot is the normal Mainland, Taiwan, Hong Kong, Vietnamese form. Only Korea insists on having a dot (but even Korea is not willing to follow the prescription of normative dictionaries to the extreme and demand the lower component to be an 曰 instead of an 日).
However, Japan was different here: while any other region standardized into one option or the other, Japan picked both. In fact, it decided to 'simplify' (pick the dot-less form) for a limited number of characters (basically, those that were a part of jōyō kanji list before the extension of 2010) but 'not simplify' (have a dot) for all the rest. So, now there is a distinction between the spellings for the 'frequent' and the 'remaining' characters in Japan.
Specifically:
So, in fact, currently the correct orthography in Japan contains the dot for two particular jōyō kanji, 賭 and 箸, which were both added to the list in 2010 only.
The non-jōyō characters are supposed to be written all with a dot, as if 'unsimplified', though for the characters allowed in personal names both forms are provided, like 猪 and 猪, and even the jōyō characters without a dot are allowed in a dot form when in names: 者.
All of this is about printed text. In manual writing, no dot:
