Beside is the more popular usage, but I have seen many references and usages of besides, as well. Beside is a preposition, and besides can be either a preposition or an adverb.
Which would be the correct usage?
I agree entirely with Sven Yargs except that I think, 'beside the point' means to be 'off the point' rather than next to it.
Example: At the Olympics, the winners stand on the podium. If you stand beside the podium then you are off it.
I say that 'beside the point' is correct for the reasons given by Sven Yargs. In particular, quote - Technically, besides the point means "in addition to or aside from the point," while idiomatically beside the point means "irrelevant."
The following ngram backs up this choice. I notice that the alternative version appears to be there as well, however on reading the associated quotes, I see that is used in a different sense.
The most basic explanation for this topic is the following;
If someone is making an argument and you understood that argument but came up with a different conclusion, then your conclusion is beside the point. In other words, your conclusion is not necessarily irrelevant, you simply missed the point. Often times a simple misunderstanding of some details or nuance. You took the same path but somehow didn't arrive on the same point.
We should help them so we can receive rewards.
That's beside the point of helping.
Now if you argued against someone's argument and arrived on the same conclusion, then your argument is besides the point. Most of the time, this means you're arguing semantics. Other times you simply want attention to your path that lead to the point instead of focusing on the path presented by someone else. You arrive on the same point but took a different path.
We need to help them because we're good people.
Isn't helping people about selflessness?
That's besides the point of being good.
So it really depends on the context of your intention and what you're trying to convey. I hope this helps.