No, not like that.
No, not like that, either. It's PYOOnee. Yes, exactly the same as puny.
And so what does puisne mean?
Well, as it happens it means something dangerously close to puny. It doesn't quite mean physically weak and scrawny, but it does mean of lower rank, and it does imply of less power.
Puisne is usually used (though I'm using the word usually here to mean more than in any other case, rather than often) to describe a subordinate judge.
Illustration by John Kay. The one on the right is Lord Monboddo, judge and founder of modern historical comparative linguistics.
I must here remind the reader, though, that describing any sort of judge as something that sounds like puny is an act of utter, utter madness.
Word Not To Use Today: puisne. Even if you do say this word then everyone will think you mean puny, so it really is a complete waste of time. The word comes from Anglo-French, from Old French puisné, born later, which is from puis, at a later date, and né, born.