2.4.2. Innermost Intercostal Muscles Proper
The second set of innermost intercostal muscles are positioned laterally within the intercostal spaces of the ribcage. These are the true innermost intercostal muscles, so for clarification I will refer to them as the 'innermost intercostal muscles proper'. The accompanying diagram shows only two examples of the innermost intercostal muscles - as you can see, they closely follow most of the shaft of the rib.
Origin: inferior border of rib above (same as internal intercostal muscles).
Insertion: superior border of rib below (same as internal intercostal muscles).
Fibre direction: inferolateral (same as internal intercostal muscles).
Nerves: intercostal nerves (ventral rami of T1 - T11).
Action: assists external and internal intercostal muscles in respiration. This seems a bit general, but these muscles can have slightly different functions depending on whether they lie more in a more anterior or posterior position.
Literature is not entirely clear on the origin and insertion of these muscle fibres. However, as you can see, the general consensus seems to be that they run in the same direction as the internal intercostal muscles.