subs. (colloquial).A diminutive midshipman.
1833. MARRYAT, Peter Simple, I. x. Clap on here, Peg, cried the woman to another, and lets have this little MIDSHIPMITE; I vants a baby to dry nurse.
1877. W. S. GILBERT, Bab Ballads, Yarn of the Nancy Bell. A bosun tight and a MIDSHIPMITE.