How to apply for the priority of invention patent and new utility model patent on the same day

First of all, it is necessary to explain whether it is the same applicant. Then apply for invention A and utility model B on the same day. From your description, it seems that they claim priority to each other. Does this make sense?

It makes sense if Invention C claims the priority of (A or B) after the filing date. C claims the priority of A, then A is deemed to be withdrawn. But the filing date (priority date) of C is the same as that of B. If it is the same applicant and the same invention, the applicant is required to choose between invention C and utility model B! Here ABC three are all the same applicants. If AB is a different applicant, that's another situation ~