Alexis Secret Path (ASP for short) is basically a Layla PT, buuuut with a difference... you need to be rude to Alexis from the get go (I don't like that, btw, I wish it would work just by not having sex with her) in the plane and not interact with her basically, it also requires you to be friends, but not too much with Erynn, and you need to be on Layla's path... since you'll get a different scene once Layla invites you to the jacuzzi the 1st time, you'll get an Alexis & Erynn scene, instead of a scene with the mom.
What it does is that Erynn talks to Alexis about you and kinda pushes her to date you, so even tho you haven't interacted with Alexis all that much and you're basically on Layla's PT, she'll start falling for you anyways, but she's very reticent because she knows Layla likes you.
Sooo it has a bigger drama potential down the road in terms of the two sisters. Oh the ASP is also the only other path where you can go to the beach in the last episode (you get invited because Erynn is pushing Alexis to flirt with you), so it's maybe the more content-full PT?
It's unclear why it exists tbh... I guess we could speculate whether it'll lead to a Layla/Alexis throuple, but that's VERY unlikely given how jealous and clingy Alexis is... plus Nyx has a no-no policy on incest anyways, so my best guess is just more extra-drama for the sisters.
OR, it's maybe a much slower Alexis path where you don't hook up with her from the begining... that might actually be the reason why it exists, there's always people complaining about relationships that develop too quickly in AVNs (even tho I don't think it applies to this game).