Split-mouth designs are frequently used in dental clinical research, where a mouth is divided into two or more experimental segments that are randomly assigned to different treatments. For full details, see the link: Split mouth experimental design - Bing . In order to calculate a sample size, one would need at minimum the research question(s), the number and kind of treatments employed, the number of segments per mouth and so on as described in: Split mouth experimental design - Bing
Further, they depend on the type of Biostatical sample one wishes to employ, some examples are given here:
📷📷 Split-mouth designs in orthodontics: an overview with ...
Thus without further information it is impossible to recommend a reasonable method for calculating an appropriate sample size. I suggest that you look at the above citations make some choices in things like a reasonable type of design employing split-mouth and return with your question.