Disputes over the same patent

It depends on whether B's patent belongs to the scope of A's claim and whether it belongs to the patent seeking part.

If it is similar, the infringement is established. If B has been put into production, it is necessary to compensate A or use the patent.

If they are not similar, B can apply for a patent without infringing A's patent right.

This does not involve priority, and the application date of A is subject to the first application.

As you said, B's creation may be similar to A's. B's patent application was unsuccessful. If it is used, A can sue you for infringement. Continued use requires authorization from a.