Fromback-pat +‎-y.

back-patty (comparativemoreback-patty,superlativemostback-patty)

1. (idiomatic)Self-congratulatory orself-aggrandizing.
   • 1969 May, book review,The Strayed Reveller, number 3, page 7:

     We can all start off feelingback-patty and warm with our secret selves, having identified a literary allusion.

   • 2018, Elizabeth Foley, Beth Coates,What Would Cleopatra Do?: Life Lessons from 50 of History's Most Extraordinary Women,page102:

     But before we get allback-patty about our leaps and bounds in the progress of human endeavor, it is worth remembering that the world of science can seem extraordinarily backward when it comes to those with two X chromosomes.

   • 2018 April 5, Marc T. Michael, “In A State Of His Own”, inThe Pulse, page16:

     So what's got me feeling mildly smug andback-patty today?

• pat on the back