What is the ruling on specifying numbers for dhikr or reciting the Beautiful Names of Allah in a particular order to obtain a specific reward?

This is not permissible, and whoever believes it to be so is engaging in innovation (bid‘ah). Any remembrance (dhikr) that is restricted by a specific number, place, time, or method not mentioned in the Sharia (definition) is an innovation. As for worshipping through the Beautiful Names of Allah, it is done by supplicating to Allah with them, as He says: (And to Allah belong the best names, so invoke Him by them), and not merely by reciting them in a specific order.