Here is the specific wording from the rule book on page 38. Some additional distinction to be made toward the bottom on other effects noted:
Minimal Damage: Some units in Alpha Strike deliver damage
on a scale so low that their attacks can potentially have no effect.
This typically occurs with lightly armed units, such as ProtoMechs,
which typically rely on numbers to make up for their limited
firepower. Units that fall into this category will feature a damage
value of “0*” (zero, with an asterisk) at the appropriate range
bracket. This value indicates that the unit can deliver minimal
damage at that range, rather than no damage at all.
Every time a unit executes a successful attack at a range bracket
with 0* damage, its controlling player must make a 1D6 roll. If the
result is 4 or higher, the attack delivers a single point of standard
damage. Otherwise, the attack still hits, but delivers no damage.
Successful minimal damage attacks that fail to deliver any actual
damage may not resolve any Critical Hit or Motive Hit checks,
but will prompt hull breach checks if they occur in underwater
or vacuum environments. In the case of special rules that modify
a unit’s damage and require rounding, minimal damage attacks
always round down to 0.