He married Caesonia; their known children include a son, Sextus Cocceius Severianus;
Sextus Cocceius Vibianus (flourished c. 204), is a known grandson.[4]
^Werner Eck, "Die Fasti consulares der Regierungszeit des Antoninus Pius, eine Bestandsaufnahme seit Géza Alföldys Konsulat und Senatorenstand" in Studia epigraphica in memoriam Géza Alföldy, hg. W. Eck, B. Feher, and P. Kovács (Bonn, 2013), p. 75 n. 20