Wikipedia
Crosspicking is a technique for playing the mandolin or guitar using a plectrum or flatpick in a rolling, syncopated style across three strings. This style is probably best known as one element of the flatpicking style in bluegrass music, and it closely resembles a banjo roll, the main difference being that the banjo roll is fingerpicked rather than flatpicked.
A typical element of the technique is the use of three pitches played repeatedly within a four-pulse rhythm. This results in a continual shifting of the pitches vis-a-vis the accented pulse. The three pitches are usually played on three adjacent strings—one per string. The pick direction can vary, depending on the required emphasis and the melody.
Mandolin player Jesse McReynolds used a crosspicking roll of down - up - up / down - up - up... creating a repeating pattern of notes that expresses the melody. Guitarist George Shuffler used a pick pattern of down - down - up / down - down- up / down - up.
The traditional banjo roll form is down - down - up / down - down - up / down - down - up . . . ; this helps to accentuate the "threes" nature of the pattern against the "four" rhythm.
The other way is using strict alternate picking: down - up - down / up - down - up / down - up - down . . . . This may be more comfortable for players who are using alternate picking for most of their playing. In actuality, one (or more) of the three pitches may be varied from one repetition of the pattern to the next, for instance the top note could be toggled up and down one step.