The phrase that encompasses organizing evidence logically in a persuasive text, putting the least important piece of evidence first, including a counterargument, and providing at least three pieces of evidence to support the argument is often referred to as "structuring a persuasive argument using the rebuttal method."
In this approach, you present your argument, follow with a counterargument, and then provide evidence in a way that strengthens your position while addressing potential objections. The systematic layout enhances clarity and persuasion in your writing.