Under what authority do I reject any of them?
You can't. You only have the authority to count them. Members of Congress can make motions to be ruled on under parliamentary procedure and the rules of Congress, all of which could be overruled by full vote of the floor. Congress can also reject Electors which would prohibit them from being counted in the total. But the Vice President in his or her capacity of presiding over the count has zero unilateral authority to do anything - never has, never will. The States and Congress have plenary power over their respective roles in sending and accepting the Electoral College votes.
Still amazed at how people just make stuff up and assign secret magic powers to the Vice President.
Here's another way of puting it another FReeper put it:
This “case” (which is actually not one) is Constitutional science fiction.
The “election” alleged to be fraudulent has no Constitutional existence. The 50 State Legislatures which appoint 535 Electors (and Congress, which appoints 3) have all adopted the custom of having people voting as the means by which the appointments are normally made, but this creates 51 elections, not one.
Those 51 elections occur at the direction of, and are subservient to, 50 legislatures and Congress. The States unwisely granted Congress 3 Electors by ratifying the XXIII Amendment in 1960, so Congress does have supervisory power OVER THOSE THREE, but not otherwise.
There is only one Presidential election in the Constitution, it takes place in December, there are 538 voters, and in December 2020 Biden got 306 of them and was elected President.
No State Legislature objected that its Electors were not the ones they had appointed. No State Legislature even convened to consider the matter. In the case of Pennsylvania, the Legislature fled to avoid considering the matter.
It has never been alleged that a single one of the 306 votes for Biden/Harris was a forgery, that the Electors who casted them were impersonating someone else, or that the Legislatures had secretly appointed other Electors.
There is zero space for an allegation of fraud in the Constitutional Presidential election of December 14, 2020.
As far as the 51 elections which occurred on November 3, 2020, they may very well have been rife with fraud, but since the appointment power of the 50 State Legislatures (535) and Congress (3) is plenary, that’s a problem for those legislatures to deal with should they choose to do so. https://freerepublic.com/focus/f-news/4133096/posts#3