In the old days folks played with 4 fingers and the thumb was held behind the keyboard. The 24343242 is an example of the old-school fingerings.
The technique utilised 3 hand positions (fingers pointing down, parallel to the keyboard, pointing up) and required the player to know when to change them. As an example, Basurmanov's 3-year bayan course is based on slowly building such a technique.
The technique held up until probably 1960-70s by which point it was finally widely considered to be obsolete.
If you look at old scores, they will have the old fingerings. Newer ones will be geared for 5.
Beware that if the scores are very old, fingers can be marked 1,2,3,4 for index, middle, ring, pinky - back then they did not even give the thumb a number. Later it started making rare appearances as 0.
A 5-finger 3-row technique was then developed. For example, Bardin suggests 23412312 for Cmaj. The hand is mainly held in second position, i.e. parallel to the keyboard.
Unless you're missing a thumb, you're better off learning the 5-fingered one.
