Yes, you can find the most stable Linux edition. The thing you need to know is that you can find the one that exactly fits for you and your expectations. Earlier we checked for The Most Popular Linux Distributions Compared.
Different Linux Distros have different releases and update cycles. For example Fedora is focusing mostly to update all apps an packages, so you will have the greatest and the latest. Some other Linux Distros like Debian prefer to delay certain updates and test them many times before they are sure that everything works smooth.
From other side, you might want to take a look at Slackware. Not that Slackware is not a modern type of Linux Distro. Slackware is one of the oldest Linux and you might need to lear more command lines if you want to get the most of it.
Talking about Slackware there is a saying through Linux users: If you know Red Hat, then you know Red Hat. If you know Slackware, then you know Linux.
Slackware as the one of the oldest, has been around here more time than others, so its considered as a parent and one of the most stable. But as I said before you might light Debian which is considered stable and always super tested compared to other editions.
In the end, we can recommend you to check the parent Linux Distros, like Slackware, Red Hat, Debian, Arch-Linux. Note that the most stable versions are not used to have an easy graphical interface. You will have to use a lot of command lines.
You should start with this article that will help you: How to choose the Best Linux Distribution